### Archive

Archive for the ‘math education’ Category

## Book out for early review

I’m happy to say that the book I’m writing with Rachel Schutt called Doing Data Science is officially out for early review. That means a few chapters which we’ve deemed “ready” have been sent to some prominent people in the field to see what they think. Thanks, prominent and busy people!

It also means that things are (knock on wood) wrapping up on the editing side. I’m cautiously optimistic that this book will be a valuable resource for people interested in what data scientists do, especially people interested in switching fields. The range of topics is broad, which I guess means that the most obvious complaint about the book will be that we didn’t cover things deeply enough, and perhaps that the level of pre-requisite assumptions is uneven. It’s hard to avoid.

Thanks to my awesome editor Courtney Nash over at O’Reilly for all her help!

And by the way, we have an armadillo on our cover, which is just plain cool:

## New Jersey at risk of implementing untested VAM-like teacher evaluation model

This is a guest post by Eugene Stern.

A big reason I love this blog is Cathy’s war on crappy models. She has posted multiple times already about the lousy performance of models that rate teachers based on year-to-year changes in student test scores (for example, read about it here). Much of the discussion focuses on the model used in New York City, but such systems have been, or are being, put in place all over the country. I want to let you know about the version now being considered for use across the river, in New Jersey. Once you’ve heard more, I hope you’ll help me try to stop it.

VAM Background

A little background if you haven’t heard about this before. Because it makes no sense to rate teachers based on students’ absolute grades or test scores (not all students start at the same place each year), the models all compare students’ test scores against some baseline. The simplest thing to do is to compare each student’s score on a test given at the end of the school year against their score on a test given at the end of the previous year. Teachers are then rated based on how much their students’ scores improved over the year.

Comparing with the previous year’s score controls for the level at which students start each year, but not for other factors beside the teacher that affect how much they learn. This includes attendance, in-school environment (curriculum, facilities, other students in the class), out-of-school learning (tutoring, enrichment programs, quantity and quality of time spent with parents/caregivers), and potentially much more. Fancier models try to take these into account by comparing each student’s end of year score with a predicted score. The predicted score is based both on the student’s previous score and on factors like those above. Improvement beyond the predicted score is then attributed to the teacher as “value added” (hence the name “value-added models,” or VAM) and turned into a teacher rating in some way, often using percentiles. One such model is used to rate teachers in New York City.

It’s important to understand that there is no single value-added model, rather a family of them, and that the devil is in the details. Two different teacher rating systems, based on two models of the predicted score, may perform very differently – both across the board, and in specific locations. Different factors may be more or less important depending on where you are. For example, income differences may matter more in a district that provides few basic services, so parents have to pay to get extracurriculars for their kids. And of course the test itself matters hugely as well.

Testing the VAM models

Teacher rating models based on standardized tests have been around for 25 years or so, but two things have happened in the last decade:

1. Some people started to use the models in formal teacher evaluation, including tenure decisions.
2. Some (other) people started to test the models.

This did not happen in the order that one would normally like. Wanting to make “data-driven decisions,” many cities and states decided to start rating teachers based on “data” before collecting any data to validate whether that “data” was any good. This is a bit like building a theoretical model of how cancer cells behave, synthesizing a cancer drug in the lab based on the model, distributing that drug widely without any trials, then waiting around to see how many people die from the side effects.

The full body count isn’t in yet, but the models don’t appear to be doing well so far. To look at some analysis of VAM data in New York City, start here and here. Note: this analysis was not done by the city but by individuals who downloaded the data after the city had to make it available because of disclosure laws.

I’m not aware of any study on the validity of NYC’s VAM ratings done by anyone actually affiliated with the city – if you know of any, please tell me. Again, the people preaching data don’t seem willing to actually use data to evaluate the quality of the systems they’re putting in place.

Assuming you have more respect for data than the mucky-mucks, let’s talk about how well the models actually do. Broadly, two ways a model can fail are being biased and being noisy. The point of the fancier value-added models is to try to eliminate bias by factoring in everything other than the teacher that might affect a student’s test score. The trouble is that any serious attempt to do this introduces a bunch of noise into the model, to the degree that the ratings coming out look almost random.

You’d think that a teacher doesn’t go from awful to great or vice versa in one year, but the NYC VAM ratings show next to no correlation in a teacher’s rating from one year to the next. You’d think that a teacher either teaches math well or doesn’t, but the NYC VAM ratings show next to no correlation in a teacher’s rating teaching a subject to one grade and their rating teaching it to another – in the very same year!  (Gary Rubinstein’s blog, linked above, documents these examples, and a number of others.)  Again, this is one particular implementation of a general class of models, but using such noisy data to make significant decisions about teachers’ careers seems nuts.

What’s happening in New Jersey

With all this as background, let’s turn to what’s happening in New Jersey.

You may be surprised that the version of the model proposed by Chris Christie‘s administration (the education commissioner is Christie appointee Chris Cerf, who helped put VAM in place in NYC) is about the simplest possible. There is no attempt to factor out bias by trying to model predicted scores, just a straight comparison between this year’s standardized test score and last year’s.  For an overview, see this.

In more detail, the model groups together all students with the same score on last year’s test, and represents each student’s progress by their score on this year’s test, viewed as a percentile across this group. That’s it. A fancier version uses percentiles calculated across all students with the same score in each of the last several years. These can’t be calculated explicitly (you may not find enough students that got exactly the same score each the last few years), so they are estimated, using a statistical technique called quantile regression.

By design, both the simple and the fancy version ignore everything about a student except their test scores. As a modeler, or just as a human being, you might find it silly not to distinguish between a fourth grader in a wealthy suburb who scored 600 on a standardized test from a fourth grader in the projects with the same score. At least, I don’t know where to find a modeler who doesn’t find it silly, because nobody has bothered to study the validity of using this model to rate teachers. If I’m wrong, please point me to a study.

Politics and SGP

But here we get into the shell game of politics, where rating teachers based on the model is exactly the proposal that lies at the end of an impressive trail of doubletalk.  Follow the bouncing ball.

These models, we are told, differ fundamentally from VAM (which is now seen as somewhat damaged goods politically, I suspect). While VAM tried to isolate teacher contribution, these models do no such thing – they are simply measuring student progress from year to year, which, after all, is what we truly care about. The models have even been rebranded with a new name: student growth percentiles, or SGP. SGP is sold as just describing student progress rather than attributing it to teachers, there can’t be any harm in that, right? – and nothing that needs validation, either. And because SGP is such a clean methodology – if you’re looking for a data-driven model to use for broad “educational assessment,” don’t get yourself into that whole VAM morass, use SGP instead!

Only before you know it, educational assessment turns into, you guessed it, rating teachers. That’s right: because these models aren’t built to rate teachers, they can focus on the things that really matter (student progress), and thus end up being – wait for it – much better for rating teachers! War is peace, friends. Ignorance is strength.

Creators of SGP

You can find a good discussion of SGP’s and their use in evaluation here, and a lot more from the same author, the impressively prolific Bruce Baker, here.  Here’s a response from the creators of SGP. They maintain that information about student growth is useful (duh), and agree that differences in SGP’s should not be attributed to teachers (emphasis mine):

Large-scale assessment results are an important piece of evidence but are not sufficient to make causal claims about school or teacher quality.

SGP and teacher evaluations

But guess what?

The New Jersey Board of Ed and state education commissioner Cerf are putting in place a new teacher evaluation code, to be used this coming academic year and beyond. You can find more details here and here.

Summarizing: for math and English teachers in grades 4-8, 30% of their annual evaluation next year would be mandated by the state to come from those very same SGP’s that, according to their creators, are not sufficient to make causal claims about teacher quality. These evaluations are the primary input in tenure decisions, and can also be used to take away tenure from teachers who receive low ratings.

The proposal is not final, but is fairly far along in the regulatory approval process, and would become final in the next several months. In a recent step in the approval process, the weight given to SGP’s in the overall evaluation was reduced by 5%, from 35%. However, the 30% weight applies next year only, and in the future the state could increase the weight to as high as 50%, at its discretion.

Modeler’s Notes

Modeler’s Note #1: the precise weight doesn’t really matter. If the SGP scores vary a lot, and the other components don’t vary very much, SGP scores will drive the evaluation no matter what their weight.

Modeler’s Note #2: just reminding you again that this data-driven framework for teacher evaluation is being put in place without any data-driven evaluation of its effectiveness. And that this is a feature, not a bug – SGP has not been tested as an attribution tool because we keep hearing that it’s not meant to be one.

In a slightly ironic twist, commissioner Cerf has responded to criticisms that SGP hasn’t been tested by pointing to a Gates Foundation study of the effectiveness of… value-added models.  The study is here.  It draws pretty positive conclusions about how well VAM’s work.  A number of critics have argued, pretty effectively, that the conclusions are unsupported by the data underlying the study, and that the data actually shows that VAM’s work badly.  For a sample, see this.  For another example of a VAM-positive study that doesn’t seem to stand up to scrutiny, see this and this.

Modeler’s Role Play #1

Say you were the modeler who had popularized SGP’s.  You’ve said that the framework isn’t meant to make causal claims, then you see New Jersey (and other states too, I believe) putting a teaching evaluation model in place that uses SGP to make causal claims, without testing it first in any way. What would you do?

So far, the SGP mavens who told us that “Large-scale assessment results are an important piece of evidence but are not sufficient to make causal claims about school or teacher quality” remain silent about the New Jersey initiative, as far as I know.

Modeler’s Role Play #2

Now you’re you again, and you’ve never heard about SGP’s and New Jersey’s new teacher evaluation code until today.  What do you do?

I want you to help me stop this thing.  It’s not in place yet, and I hope there’s still time.

I don’t think we can convince the state education department on the merits.  They’ve made the call that the new evaluation system is better than the current one or any alternatives they can think of, they’re invested in that decision, and we won’t change their minds directly.  But we can make it easier for them to say no than to say yes.  They can be influenced – by local school administrators, state politicians,  the national education community, activists, you tell me who else.  And many of those people will have more open minds.  If I tell you, and you tell the right people, and they tell the right people, the chain gets to the decision makers eventually.

I don’t think I could convince Chris Christie, but maybe I could convince Bruce Springsteen if I met him, and maybe Bruce Springsteen could convince Chris Christie.

VAM-anifesto

I thought we could start with a manifesto – a direct statement from the modeling community explaining why this sucks. Directed at people who can influence the politics, and signed by enough experts (let’s get some big names in there) to carry some weight with those influencers.

Can you help? Help write it, sign it, help get other people to sign it, help get it to the right audience. Know someone whose opinion matters in New Jersey? Then let me know, and help spread the word to them. Use Facebook and Twitter if it’ll help. And don’t forget good old email, phone calls, and lunches with friends.

Or, do you have a better idea? Then put it down. Here. The comments section is wide open. Let’s not fall back on criticizing the politicians for being dumb after the fact.  Let’s do everything we can to keep them from doing this dumb thing in the first place.

Shame on us if we can’t make this right.

## Guest post: Kaisa Taipale visualizes mathematics Ph.D.’s emigration patterns

This is a guest post by Kaisa Taipale. Kaisa got a BS at Caltech, a Ph.D. in math at the University of Minnesota, was a post-doc at MSRI, an assistant professor at St. Olaf College 2010-2012, and is currently visiting Cornell, which is where I met here a couple of weeks ago, and where she told me about her cool visualizations of math Ph.D. emigration patterns and convinced her to write a guest post. Here’s Kaisa on a bridge:

Math data and viz

I was inspired by this older post on Mathbabe, about visualizing the arXiv postings of various math departments.

It got me thinking about tons of interesting questions I’ve asked myself and could answer with visualizations: over time, what’s been coolest on the arXiv? are there any topics that are especially attractive to hiring institutions? There’s tons of work to do!

I had to start somewhere though, and as I’m a total newbie when it comes to data analysis, I decided to learn some skills while focusing on a data set that I have easy non-technical access to and look forward to reading every year. I chose the AMS Annual Survey. I also wanted to stick to questions really close to my thoughts over the last two years, namely the academic job search.

I wanted to learn to use two tools, R and Circos. Why Circos? See the visualizations of college major and career path here - it’s pretty! I’ve messed around with a lot of questions, but in this post I’ll look at two and a half.

Graduating PhDs

Where do graduating PhDs from R1 universities end up, in the short term? I started with graduates of public R1s, as I got my PhD at one.

The PhD-granting institutions are colored green, while academic institutions granting other degrees are in blue. Purple is for business, industry, government, and research institutions. Red is for non-U.S. employment or people not seeking — except for the bright red, which is still seeking. Yellow rounds things out at unknown. Remember, these figures are for immediate plans after graduation rather than permanent employment.

While I was playing with this data (read “learning how to use the reshape and ggplot2 packages”) I noticed that people from private R1s tend to end up at private R1s more often. So I graphed that too.

Does the professoriate in the audience have any idea if this is self-selection or some sort of preference on the part of employers? Also, what happened between 2001 and 2003? I was still in college, and have no idea what historical events are at play here.

Where mathematicians go

For any given year, we can use a circular graph to show us where people go. This is a more clumped version of the above data from 2010 alone, plotted using Circos. (Supplemental table E.4 from the AMS report online.)

The other question – the question current mathematicians secretly care more about, in a gossipy and potentially catty way – is what fields lead to what fate. We all know algebra and number theory are the purest and most virtuous subjects, and applied math is for people who want to make money or want to make a difference in the world.

[On that note, you might notice that I removed statistics PhDs in the visualization below, and I also removed some of the employment sectors that gained only a few people a year. The stats ribbons are huge and the small sectors are very small, so for looks alone I took them out.]

Higher resolution version available here.

Wish list

I wish I could animate a series of these to show this view over time as well. Let me know if you know how to do that! Another nice thing I could do would be to set up a webpage in which these visualizations could be explored in a bit more depth. (After finals.)

Also:

• I haven’t computed any numbers for you
• the graphs from R show employment in each field by percentage of graduates instead of total number per category;
• it’s hard to show both data over time and all the data one could explore. But it’s a start.

I should finish with a shout-out to Roger Peng and Jeff Leek, though we’ve never met: I took Peng’s Computing for Data Analysis and much of Leek’s Data Analysis on Coursera (though I’m one of those who didn’t finish the class). Their courses and Stack Overflow taught me almost everything I know about R. As I mentioned above, I’m pretty new to this type of analysis.

What questions would you ask? How can I make the above cooler? Did you learn anything?

## Value-added model doesn’t find bad teachers, causes administrators to cheat

There’ve been a couple of articles in the past few days about teacher Value-Added Testing that have enraged me.

If you haven’t been paying attention, the Value-Added Model (VAM) is now being used in a majority of the states (source: the Economist):

But it gives out nearly random numbers, as gleaned from looking at the same teachers with two scores (see this previous post). There’s a 24% correlation between the two numbers. Note that some people are awesome with respect to one score and complete shit on the other score:

Final thing you need to know about the model: nobody really understands how it works. It relies on error terms of an error-riddled model. It’s opaque, and no teacher can have their score explained to them in Plain English.

Now, with that background, let’s look into these articles.

First, there’s this New York Times article from yesterday, entitled “Curious Grade for Teachers: Nearly All Pass”. In this article, it describes how teachers are nowadays being judged using a (usually) 50/50 combination of classroom observations and VAM scores. This is different from the past, which was only based on classroom observations.

What they’ve found is that the percentage of teachers found “effective or better” has stayed high in spite of the new system – the numbers are all over the place but typically between 90 and 99 percent of teachers. In other words, the number of teachers that are fingered as truly terrible hasn’t gone up too much. What a fucking disaster, at least according to the NYTimes, which seems to go out of its way to make its readers understand how very much high school teachers suck.

A few things to say about this.

1. Given that the VAM is nearly a random number generator, this is good news – it means they are not trusting the VAM scores blindly. Of course, it still doesn’t mean that the right teachers are getting fired, since half of the score is random.
2. Another point the article mentions is that failing teachers are leaving before the reports come out. We don’t actually know how many teachers are affected by these scores.
3. Anyway, what is the right number of teachers to fire each year, New York Times? And how did you choose that number? Oh wait, you quoted someone from the Brookings Institute: “It would be an unusual profession that at least 5 percent are not deemed ineffective.” Way to explain things so scientifically! It’s refreshing to know exactly how the army of McKinsey alums approach education reform.
4. The overall article gives us the impression that if we were really going to do our job and “be tough on bad teachers,” then we’d weight the Value-Added Model way more. But instead we’re being pussies. Wonder what would happen if we weren’t pussies?

The second article explained just that. It also came from the New York Times (h/t Suresh Naidu), and it was a the story of a School Chief in Atlanta who took the VAM scores very very seriously.

What happened next? The teachers cheated wildly, changing the answers on their students’ tests. There was a big cover-up, lots of nasty political pressure, and a lot of good people feeling really bad, blah blah blah. But maybe we can take a step back and think about why this might have happened. Can we do that, New York Times? Maybe it had to do with the $500,000 in “performance bonuses” that the School Chief got for such awesome scores? Let’s face it, this cheating scandal, and others like it (which may never come to light), was not hard to predict (as I explain in this post). In fact, as a predictive modeler, I’d argue that this cheating problem is the easiest thing to predict about the VAM, considering how it’s being used as an opaque mathematical weapon. ## Nerd Nite: A Drunken Venue for Ideas March 26, 2013 2 comments MathBabe recently wrote an article critical of the elitist nature of Ted Talks, which you can read here. Fortunately for her, and for the hoi polloi everywhere clamoring for populist science edutainment, there is an alternative: Nerd Nite. Once a month, in cities all over the globe, nerds herd into a local bar and turn it into a low-brow forum for innovative science ideas. Think Ted Talks on tequila. Each month, three speakers present talks for 20-30 minutes, followed by questions and answers from the invariably sold-out audience. The monthly forum gives professional and amateur scientists an opportunity to explain their fairly abstruse specialties accessibly to a lay audience – a valuable skill. Since the emphasis is on science entertainment, it also gives the speakers a chance to present their ideas in a more engaging way: in iambic pentameter, in drag with a tuba, in three-part harmony, or via interpretive dance – an invaluable skill. The resulting atmosphere is informal, delightfully debauched, and refreshingly pro-science. Slaking our thirst for both science education and mojitos, Nerd Nite started small but quickly went viral. Nerd Nites are now being held in 50 cities, from San Francisco to Kansas City and Auckland to Liberia. You can find the full listing of cities here; if you don’t see one near you, start one! Last Wednesday night I was twitterpated to be one of three guest nerds sharing the stage at San Francisco’s Nerd Nite. I put the chic back into geek with a biology talk entitled “Genital Plugs, Projectile Penises, and Gay Butterflies: A Naturalist Explains the Birds and the Bees.” A video recording of the presentation will be available online soon, but in the meantime, here’s a tantalizing clip from the talk, in which Isabella Rossellini explains the mating habits of the bee. Warning: this is scientifically sexy. I shared the stage with Chris Anderson, who gave a fascinating talk on how the DIY community is building drones out of legos and open-source software. These DIY drones fly below government regulation and can be used for non-military applications, something we hear far too little of in the daily war digest that passes for news. The other speaker was Mark Rosin of the UK-based Guerrilla Science project. This clever organization reaches out to audiences at non-science venues, such as music concerts, and conducts entertaining presentations that teach core science ideas. As part of his presentation Mark used 250 inflated balloons and a bass amp to demonstrate the physics concept of resonance. If your curiosity has been piqued and you’d like to check out an upcoming Nerd Nite, consider attending the upcoming Nerdtacular, the first Nerd Nite Global Festival, to be held this August 16-18th in Brooklyn, New York. The global Nerdtacular: Now that’s an idea worth spreading. ## The overburdened prior At my new job I’ve been spending my time editing my book with Rachel Schutt (who is joining me at JRL next week! Woohoo!). It’s called Doing Data Science and it’s based on these notes I took when she taught a class on data science at Columbia last semester. Right now I’m working on the alternating least squares chapter, where we learned from Matt Gattis how to build and optimize a recommendation system. A very cool algorithm. However, to be honest I’ve started to feel very sorry for the one parameter we call $\lambda.$ It’s also sometimes referred to as “the prior”. Let me tell you, the world is asking too much from this little guy, and moreover most of the big-data world is too indifferent to its plight. Let me explain. $\lambda$ as belief First, he’s supposed to reflect an actual prior belief – namely, his size is supposed to reflect a mathematical vision of how big we think the coefficients in our solution should be. In an ideal world, we would think deeply about this question of size before looking at our training data, and think only about the scale of our data (i.e. the input), the scale of the preferences (i.e. the recommendation system output) and the quality and amount of training data we have, and using all of that, we’d figure out our prior belief on the size or at least the scale of our hoped-for solution. I’m not statistician, but that’s how I imagine I’d spend my days if I were: thinking through this reasoning carefully, and even writing it down carefully, before I ever start my training. It’s a discipline like any other to carefully state your beliefs beforehand so you know you’re not just saying what the data wants to hear. $\lambda$ as convergence insurance But then there’s the next thing we ask of our parameter $\lambda,$ namely we assign him the responsibility to make sure our algorithm converges. Because our algorithm isn’t a closed form solution, but rather we are discovering coefficients of two separate matrices $U$ and $V$, fixing one while we tweak the other, then switching. The algorithm stops when, after a full cycle of fixing and tweaking, none of the coefficients have moved by more than some pre-ordained $\epsilon.$ The fact that this algorithm will in fact stop is not obvious, and in fact it isn’t always true. It is (mostly*) true, however, if our little $\lambda$ is large enough, which is due to the fact that our above-mentioned imposed belief of size translates into a penalty term, which we minimize along with the actual error term. This little miracle of translation is explained in this post. And people say that all the time. When you say, “hey what if that algorithm doesn’t converge?” They say, “oh if $\lambda$ is big enough it always does.” But that’s kind of like worrying about your teenage daughter getting pregnant so you lock her up in her room all the time. You’ve solved the immediate problem by sacrificing an even bigger goal. Because let’s face it, if the prior $\lambda$ is too big, then we are sacrificing our actual solution for the sake of conveniently small coefficients and convergence. In the asymptotic limit, which I love thinking about, our coefficients all go to zero and we get nothing at all. Our teenage daughter has run away from home with her do-nothing boyfriend. By the way, there’s a discipline here too, and I’d suggest that if the algorithm doesn’t converge you might also want to consider reducing your number of latent variables rather than increasing your $\lambda$ since you could be asking too much from your training data. It just might not be able to distinguish that many important latent characteristics. $\lambda$ as tuning parameter Finally, we have one more job for our little $\lambda$, we’re not done with him yet. Actually for some people this is his only real job, because in practice this is how he’s treated. Namely, we optimize him so that our results look good under whatever metric we decide to care about (but it’s probably the mean squared error of preference prediction on a test set (hopefully on a test set!)). In other words, in reality most of the above nonsense about $\lambda$ is completely ignored. This is one example among many where having the ability to push a button that makes something hard seem really easy might be doing more harm than good. In this case the button says “optimize with respect to $\lambda$“, but there are other buttons that worry me just as much, and moreover there are lots of buttons being built right now that are even more dangerous and allow the users to be even more big-data-blithe. I’ve said it before and I’ll say it again: you do need to know about inverting a matrix, and other math too, if you want to be a good data scientist. * There’s a change-of-basis ambiguity that’s tough to get rid of here, since you only choose the number of latent variables, not their order. This doesn’t change the overall penalty term, so you can minimize that with large enough $\lambda,$ but if you’re incredibly unlucky I can imagine you might bounce between different solutions that differ by a base change. In this case your steps should get smaller, i.e. the amount you modify your matrix each time you go through the algorithm. This is only a theoretical problem by the way but I’m a nerd. ## Good news for professors: online courses suck If this New York Times editorial is correct, and it certainly passes the smell test, students are not well-served by online courses but are by so-called “hybrid” courses, where there’s a bit of online stuff and also a bit of one-on-one time. From the editorial: The research has shown over and over again that community college students who enroll in online courses are significantly more likely to fail or withdraw than those in traditional classes, which means that they spend hard-earned tuition dollars and get nothing in return. Worse still, low-performing students who may be just barely hanging on in traditional classes tend to fall even further behind in online courses. This is important news for math departments, at least in the medium term (i.e. until machine learners figure out how to successfully simulate one-on-one interactions), because it means they won’t be replacing calculus class with a computer. And as every mathematician should know, calculus is the bread and butter of math departments. Categories: math education ## Gender bias in math I don’t agree with everything she always says, but I agree with everything Izabella Laba says in this post called Gender Bias 101 For Mathematicians (hat tip Jordan Ellenberg). And I’m kind of jealous she put it together in such a fantastic no-bullshit way. Namely, she debunks a bunch of myths of gender bias. Here’s my summary, but you should read the whole thing: 1. Myth: Sexism in math is perpetrated mainly by a bunch of enormously sexist old guys. Izabella: Nope, it’s everyone, and there’s lots of evidence for that. 2. Myth: The way to combat sexism is to find those guys and isolate them. Izabella: Nope, that won’t work, since it’s everyone. 3. Myth: If it’s really everyone, it’s too hard to solve. Izabella: Not necessarily, and hey you are still trying to solve the Riemann Hypothesis even though that’s hard (my favorite argument). 4. Myth: We should continue to debate about its existence rather than solution. Izabella: We are beyond that, it’s a waste of time, and I’m not going to waste my time anymore. 5. Myth: Izabella, you are only writing this to be reassured. Izabella: Don’t patronize me. Here’s what I’d add. I’ve been arguing for a long time that gender bias against girls in math starts young and starts at the cultural level. It has to do with expectations of oneself just as much as a bunch of nasty old men (by the way, the above is not to say there aren’t nasty old men (and nasty old women!), just that it’s not only about them). My argument has been that the cultural differences are larger than the talent differences, something Larry Summers strangely dismissed without actually investigating in his famous speech. And I think I’ve found the smoking gun for my side of this argument, in the form of an interactive New York Times graphic from last week’s Science section which I’ve screenshot here: What this shows is that 15-year-old girls out-perform 15-year-old boys in certain countries and under-perform them in others. Those countries where they outperform boys is not random and has everything to do with cultural expectations and opportunities for girls in those countries and is explained to some extent by stereotype threat. Go read the article, it’s fascinating. I’ll say again what I said already at the end of this post: the great news is that it is possible to address stereotype threat directly, which won’t solve everything but will go a long way. You do it by emphasizing that mathematical talent is not inherent, nor fixed at birth, and that you can cultivate it and grow it over time and through hard work. I make this speech whenever I can to young people. Spread the word! ## I love me some nerd girls Last night I was waiting for a bus to go hang with my Athena Mastermind group, which consists of a bunch of very cool Barnard student entrepreneurs and their would-be role models (I say would-be because, although we role models are also very cool, I often think the students are role modeling for us). As I was waiting at the bus stop, I overheard two women talking about the new Applied Data Science class that just started at Columbia, which is being taught by Ian Langmore, Daniel Krasner and Chang She. I knew about this class because Ian came to advertise it last semester in Rachel Schutt’s Intro to Data Science class which I blogged. One of the women at the bus stop had been in Rachel’s class and the other is in Ian’s. Turns out I just love overhearing nerd girls talking data science at the bus stop. Don’t you?? And to top off the nerd girl experience, I’m on my way today to Nebraska to give a talk to a bunch of undergraduate women in math about what they can do with math outside of academia. I’m planning it to be an informative talk, but that’s really just cover to its real goal, which is to give a pep talk. My experience talking to young women in math, at least when they are grad students, is that they respond viscerally to encouragement, even if it’s vague. I can actually see their egos inflate in the audience as I speak, and that’s a good thing, that’s why I’m there. As a community, I’ve realized, nerd girls going through grad school are virtually starved for positive feedback, and so my job is pretty clear cut: I’m going to tell them how awesome they are and answer their questions about what it’s like in the “real world” and then go back to telling them how awesome they are. By the end they sit a bit straighter and smile a bit more after I’m done, after I’ve told them, or reminded them at least, how much power they have as nerd girls – how many options they have, and how they don’t have to be risk-averse, and how they never need to apologize. Tomorrow my audience is undergraduates, which is a bit trickier, since as an undergrad you still get consistent feedback in the form of grades. So I will tailor my information as well as my encouragement a bit, and try not to make grad school sound too scary, because I do think that getting a Ph.D. is still a huge deal. Comment below if you have suggestions for my talk, please! ## Should the U.S. News & World Reports college ranking model be open source? I had a great time giving my “Weapons of Math Destruction” talk in San Diego, and the audience was fantastic and thoughtful. One question that someone asked was whether the US News & World Reports college ranking model should be forced to be open sourced – wouldn’t that just cause colleges to game the model? First of all, colleges are already widely gaming the model and have been for some time. And that gaming is a distraction and has been heading colleges in directions away from good instruction, which is a shame. And if you suggest that they change the model all the time to prevent this, then you’ve got an internal model of this model that needs adjustment. They might be tinkering at the edges but overall it’s quite clear what’s going into the model: namely, graduation rates, SAT scores, number of Ph.D’s on staff, and so on. The exact percentages change over time but not by much. The impact that this model has had on education and how universities apportion resources has been profound. Academic papers have been written on the law school version of this story. Moreover, the tactics that US News & World Reports uses to enforce their dominance of the market are bullying, as you can learn from the President of Reed College, which refuses to be involved. Back to the question. Just as I realize that opening up all data is not reasonable or desirable, because first of all there are serious privacy issues but second of all certain groups have natural advantages to openly shared resources, it is also true that opening up all models is similarly problematic. However, certain data should surely be open: for example, the laws of our country, that we are all responsible to know, should be freely available to us (something that Aaron Swartz understood and worked towards). How can we be held responsible for laws we can’t read? Similarly, public-facing models, such as credit scoring models and teacher value-added models, should absolutely be open and accessible to the public. If I’m being judged and measured and held accountable by some model in my daily life as a citizen, that has real impact on how my future will unfold, then I should know how that process works. And if you complain about the potential gaming of those public-facing models, I’d answer: if they are gameable then they shouldn’t be used, considering the impact they have on so many people’s lives. Because a gameable model is a weak model, with proxies that fail. Another way to say this is we should want someone to “game” the credit score model if it means they pay their bills on time every month (I wrote about this here). Back to the US News & World Report model. Is it public facing? I’m no lawyer but I think a case can be made that it is, and that the public’s trust in this model makes it a very important model indeed. Evidence can be gathered by measuring the extent to which colleges game the model, which they only do because the public cares so much about the rankings. Even so, what difference would that make, to open it up? In an ideal world, where the public is somewhat savvy about what models can and cannot do, opening up the US News & World Reports college ranking model would result in people losing faith in it. They’d realize that it’s no more valuable than an opinion from a highly vocal uncle of theirs who is obsessed with certain metrics and blind to individual eccentricities and curriculums that may be a perfect match for a non-conformist student. It’s only one opinion among many, and not to be religiously believed. But this isn’t an ideal world, and we have a lot of work to do to get people to understand models as opinions in this sense, and to get people to stop trusting them just because they’re mathematically presented. ## I don’t have to prove theorems to be a mathematician I’m giving a talk at the Joint Mathematics Meeting on Thursday (it’s a 30 minute talk that starts at 11:20am, in Room 2 of the Upper Level of the San Diego Conference Center, I hope you come!). I have to distill the talk from an hour-long talk I gave recently in the Stony Brook math department, which was stimulating. Thinking about that talk brought something up for me that I think I want to address before the next talk. Namely, at the beginning of the talk I was explaining the title, “How Mathematics is Used Outside of Academia,” and I mentioned that most mathematicians that leave academia end up doing modeling. I can’t remember the exact exchange, but I referred to myself at some point in this discussion as a mathematician outside of academia, at which point someone in the audience expressed incredulity: him: Really? Are you still a mathematician? Do you prove theorems? me: No, I don’t prove theorems any longer, now that I am a modeler… (confused look) At the moment I didn’t have a good response to this, because he was using a different definition of “mathematician” than I was. For some reason he thought a mathematician must prove theorems. I don’t think so. I had a conversation about this after my talk with Bob Beals, who was in the audience and who taught many years ago at the math summer program I did last summer. After getting his Ph.D. in math, Bob worked for the spooks, and now he works for RenTech. So he knows a lot about doing math outside academia too, and I liked his perspective on this question. Namely, he wanted to look at the question through the lens of “grunt work”, which is to say all of the actual work that goes into a “result.” As a mathematician, of course, you don’t simply sit around all day proving theorems. Actually you spend most of your time working through examples to get a feel for the terrain, and thinking up simple ways to do what seems like hard things, and trying out ideas that fail, and going down paths that are dry. If you’re lucky, then at the end of a long journey like this, you will have a theorem. The same basic thing happens in modeling. You spend lots of time with the data, getting to know it, and then trying out certain approaches, which sometimes, or often, end up giving you nothing interesting, and half the time you realize you were expecting the wrong thing so you have to change it entirely. In the end you may end up with a model which is useful. If you’re lucky. There’s a lot of grunt work in both endeavors, and there’s a lot of hard thinking along the way, lots of ways for you to fool yourself that you’ve got something when you haven’t. Perhaps in modeling it’s easier to lie, which is a big difference indeed. But if you’re an honest modeler then I claim the difference in the process of getting an interesting and important result is not that different. And, I claim, I am still being a mathematician while I’m doing it. ## I totally trust experts, actually I lied yesterday, as a friend at my Occupy meeting pointed out to me last night. I made it seem like I look into every model before trusting it, and of course that’s not true. I eat food grown and prepared by other people daily. I go on airplanes and buses all the time, trusting that they will work and that they will be driven safely. I still have my money in a bank, and I also hire an accountant and sign my tax forms without reading them. So I’m a hypocrite, big-time. There’s another thing I should clear up: I’m not claiming I understand everything about climate research just because I talked to an expert for 2 or 3 hours. I am certainly not an expert, nor am I planning to become one. Even so, I did learn a lot, and the research I undertook was incredibly useful to me. So, for example, my father is a climate change denier, and I have heard him give a list of scientific facts to argue against climate change. I asked my expert to counter-argue these points, and he did so. I also asked him to explain the underlying model at a high level, which he did. My conclusion wasn’t that I’ve looked carefully into the model and it’s right, because that’s not possible in such a short time. My conclusion was that this guy is trustworthy and uses logical argument, which he’s happy to share with interested people, and moreover he manages to defend against deniers without being intellectually defensive. In the end, I’m trusting him, an expert. On the other hand, if I met another person with a totally different conclusion, who also impressed me as intellectually honest and curious, then I’d definitely listen to that guy too, and I’d be willing to change my mind. So I do imbue models and theories with a limited amount of trust depending on how much sense they makes to me. I think that’s reasonable, and it’s in line with my advocacy of scientific interpreters. Obviously not all scientific interpreters would be telling the same story, but that’s not important – in fact it’s vital that they don’t, because it is a privilege to be allowed to listen to the different sides and be engaged in the debate. If I sat down with an expert for a whole day, like my friend Jordan suggests, to determine if they were “right” on an issue where there’s argument among experts, then I’d fail, but even understanding what they were arguing about would be worthwhile and educational. Let me say this another way: experts argue about what they don’t agree on, of course, since it would be silly for them to talk about what they do agree on. But it’s their commonality that we, the laypeople, are missing. And that commonality is often so well understood that we could understand it rather quickly if it was willingly explained to us. That would be a huge step. So I wasn’t lying after all, if I am allowed to define the “it” that I did get at in the two hours with an expert. When I say I understood it, I didn’t mean everything, I meant a much larger chunk of the approach and method than I’d had before, and enough to evoke (limited) trust. Something I haven’t addressed, which I need to think about more (please help!), is the question of what subjects require active skepticism. On of my commenters, Paul Stevens, brought this up: … For me, lay people means John Q Public – public opinion because public opinion can shape policy. In practice, this only matters for a select few issues, such as climate change or science education. There is no impact to a lay person not understanding / believing in the Higgs particle for example. ## On trusting experts, climate change research, and scientific translators Stephanie Tai has written a thoughtful response on Jordan Ellenberg’s blog to my discussion with Jordan regarding trusting experts (see my Nate Silver post and the follow-up post for more context). Trusting experts Stephanie asks three important questions about trusting experts, which I paraphrase here: 1. What does it take to look into a model yourself? How deeply must you probe? 2. How do you avoid being manipulated when you do so? 3. Why should we bother since stuff is so hard and we each have a limited amount of time? I must confess I find the first two questions really interesting and I want to think about them, but I have a very little patience with the last question. Here’s why: • I’ve seen too many people (individual modelers) intentionally deflect investigations into models by setting them up as so hard that it’s not worth it (or at least it seems not worth it). They use buzz words and make it seem like there’s a magical layer of their model which makes it too difficult for mere mortals. But my experience (as an arrogant, provocative, and relentless questioner) is that I can always understand a given model if I’m talking to someone who really understands it and actually wants to communicate it. • It smacks of an excuse rather than a reason. If it’s our responsibility to understand something, then by golly we should do it, even if it’s hard. • Too many things are left up to people whose intentions are not reasonable using this “too hard” argument, and it gives those people reason to make entire systems seem too difficult to penetrate. For a great example, see the financial system, which is consistently too complicated for regulators to properly regulate. I’m sure I seem unbelievably cynical here, but that’s where I got by working in finance, where I saw first-hand how manipulative and manipulated mathematical modeling can become. And there’s no reason at all such machinations wouldn’t translate to the world of big data or climate modeling. Climate research Speaking of climate modeling: first, it annoys me that people are using my “distrust the experts” line to be cast doubt on climate modelers. People: I’m not asking you to simply be skeptical, I’m saying you should look into the models yourself! It’s the difference between sitting on a couch and pointing at a football game on TV and complaining about a missed play and getting on the football field yourself and trying to figure out how to throw the ball. The first is entertainment but not valuable to anyone but yourself. You are only adding to the discussion if you invest actual thoughtful work into the matter. To that end, I invited an expert climate researcher to my house and asked him to explain the climate models to me and my husband, and although I’m not particularly skeptical of climate change research (more on that below when I compare incentives of the two sides), I asked obnoxious, relentless questions about the model until I was satisfied. And now I am satisfied. I am considering writing it up as a post. As an aside, if climate researchers are annoyed by the skepticism, I can understand that, since football fans are an obnoxious group, but they should not get annoyed by people who want to actually do the work to understand the underlying models. Another thing about climate research. People keep talking about incentives, and yes I agree wholeheartedly that we should follow the incentives to understand where manipulation might be taking place. But when I followed the incentives with respect to climate modeling, they bring me straight to climate change deniers, not to researchers. Do we really think these scientists working with their research grants have more at stake than multi-billion dollar international companies who are trying to ignore the effect of their polluting factories on the environment? People, please. The bulk of the incentives are definitely with the business owners. Which is not to say there are no incentives on the other side, since everyone always wants to feel like their research is meaningful, but let’s get real. Scientific translators I like this idea Stephanie comes up with: Some sociologists of science suggest that translational “experts”–that is, “experts” who aren’t necessarily producing new information and research, but instead are “expert” enough to communicate stuff to those not trained in the area–can help bridge this divide without requiring everyone to become “experts” themselves. But that can also raise the question of whether these translational experts have hidden agendas in some way. Moreover, one can also raise questions of whether a partial understanding of the model might in some instances be more misleading than not looking into the model at all–examples of that could be the various challenges to evolution based on fairly minor examples that when fully contextualized seem minor but may pop out to someone who is doing a less systematic inquiry. First, I attempt to make my blog something like a platform for this, and I also do my best to make my agenda not at all hidden so people don’t have to worry about that. This raises a few issues for me: • Right now we depend mostly on press to do our translations, but they aren’t typically trained as scientists. Does that make them more prone to being manipulated? I think it does. • How do we encourage more translational expertise to emerge from actual experts? Currently, in academia, the translation to the general public of one’s research is not at all encouraged or rewarded, and outside academia even less so. • Like Stephanie, I worry about hidden agendas and partial understandings, but I honestly think they are secondary to getting a robust system of translation started to begin with, which would hopefully in turn engage the general public with the scientific method and current scientific knowledge. In other words, the good outweighs the bad here. ## MOOCs and calculus I’ve really enjoyed the discussion on my post from yesterday about MOOCs and how I predict they are going to affect the education world. I could be wrong, of course, but I think this stuff is super interesting to think about. One thing I thought about since writing the post yesterday, in terms of math departments, is that I used to urge people involved in math departments to be attentive to their calculus teaching. The threat, as I saw it then, was this: if math departments are passive and boring and non-reactive about how they teach calculus, then other departments which need calculus for their majors would pick up the slack and we’d see calculus taught in economics, physics, and engineering departments. The reason math departments should care about this is that calculus is the bread and butter of math departments – math departments in other countries who have lost calculus to other departments are very small. If you only need to teach math majors, it doesn’t require that many people to do that. But now I don’t even bother saying this, because the threat from MOOCs is much bigger and is going to have a more profound effect, and moreover there’s nothing math departments can do to stop it. Well, they can bury their head in the sand but I don’t recommend it. Once there’s a really good calculus sequence out there, why would departments continue to teach the old fashioned way? Once there’s a fantastic calculus-for-physics MOOC, or calculus-for-economics MOOC available, one would hope that math departments would admit they can’t do better. Instead of the old-fashioned calculus approach they’d figure out a way to incorporate the MOOC and supplement it by forming study groups and leading sections on the material. This would require a totally different set-up, and probably fewer mathematicians. Another thing. I think I’ve identified a few separate issues in the discussion that it makes sense to highlight. There are four things (at least) that are all rolled together in our current college and university experience: • learning itself, • credentialing, • research, and • socializing So, MOOCs directly address learning but clearly want to control something about credentialing too, which I think won’t necessarily work. They also affect research because the role of professor as learning instructor will change. They give us nothing in terms of socializing. But as commenters have pointed out, socializing students is a huge part of the college experience, and may be even more important than credentialing. Or another way of saying that is people look at your resume not so much to know what you know but to know how you’ve been socialized. It makes me wonder how we will address the “socializing” part of education in the future. And it also makes me wonder where research will be in 100 years. Categories: math education, musing ## Columbia Data Science course, week 14: Presentations In the final week of Rachel Schutt’s Columbia Data Science course we heard from two groups of students as well as from Rachel herself. Data Science; class consciousness The first team of presenters consisted of Yegor, Eurry, and Adam. Many others whose names I didn’t write down contributed to the research, visualization, and writing. First they showed us the very cool graphic explaining how self-reported skills vary by discipline. The data they used came from the class itself, which did this exercise on the first day: so the star in the middle is the average for the whole class, and each star along the side corresponds to the average (self-reported) skills of people within a specific discipline. The dotted lines on the outside stars shows the “average” star, so it’s easier to see how things vary per discipline compared to the average. Surprises: Business people seem to think they’re really great at everything except communication. Journalists are better at data wrangling than engineers. We will get back to the accuracy of self-reported skills later. We were asked, do you see your reflection in your star? Also, take a look at the different stars. How would you use them to build a data science team? Would you want people who are good at different skills? Is it enough to have all the skills covered? Are there complementary skills? Are the skills additive, or do you need overlapping skills among team members? Thought Experiment If all data which had ever been collected were freely available to everyone, would we be better off? Some ideas were offered: • all nude photos are included. [Mathbabe interjects: it's possible to not let people take nude pics of you. Just sayin'.] • so are passwords, credit scores, etc. • how do we make secure transactions between a person and her bank considering this? • what does it mean to be “freely available” anyway? The data of power; the power of data You see a lot of people posting crap like this on Facebook: But here’s the thing: the Berner Convention doesn’t exist. People are posting this to their walls because they care about their privacy. People think they can exercise control over their data but they can’t. Stuff like this give one a false sense of security. In Europe the privacy laws are stricter, and you can request data from Irish Facebook and they’re supposed to do it, but it’s still not easy to successfully do. And it’s not just data that’s being collected about you – it’s data you’re collecting. As scientists we have to be careful about what we create, and take responsibility for our creations. As Francois Rabelais said, Wisdom entereth not into a malicious mind, and science without conscience is but the ruin of the soul. Or as Emily Bell from Columbia said, Every algorithm is editorial. We can’t be evil during the day and take it back at hackathons at night. Just as journalists need to be aware that the way they report stories has consequences, so do data scientists. As a data scientist one has impact on people’s lives and how they think. Here are some takeaways from the course: • We’ve gained significant powers in this course. • In the future we may have the opportunity to do more. • With data power comes data responsibility. Who does data science empower? The second presentation was given by Jed and Mike. Again, they had a bunch of people on their team helping out. Thought experiment Let’s start with a quote: “Anything which uses science as part of its name isn’t political science, creation science, computer science.” - Hal Abelson, MIT CS prof Keeping this in mind, if you could re-label data science, would you? What would you call it? Some comments from the audience: • Let’s call it “modellurgy,” the craft of beating mathematical models into shape instead of metal • Let’s call it “statistics” Does it really matter what data science is? What should it end up being? Chris Wiggins from Columbia contends there are two main views of what data science should end up being. The first stems from John Tukey, inventor of the fast fourier transform and the box plot, and father of exploratory data analysis. Tukey advocated for a style of research he called “data analysis”, emphasizing the primacy of data and therefore computation, which he saw as part of statistics. His descriptions of data analysis, which he saw as part of doing statistics, are very similar to what people call data science today. The other prespective comes from Jim Gray, Computer Scientist from Microsoft. He saw the scientific ideals of the enlightenment age as expanding and evolving. We’ve gone from the theories of Darwin and Newton to experimental and computational approaches of Turing. Now we have a new science, a data-driven paradigm. It’s actually the fourth paradigm of all the sciences, the first three being experimental, theoretical, and computational. See more about this here. Wait, can data science be both? Note it’s difficult to stick Computer Science and Data Science on this line. Statistics is a tool that everyone uses. Data science also could be seen that way, as a tool rather than a science. Who does data science? Here’s a graphic showing the make-up of Kaggle competitors. Teams of students collaborated to collect, wrangle, analyze and visualize this data: The size of the blocks correspond to how many people in active competitions have an education background in a given field. We see that almost a quarter of competitors are computer scientists. The shading corresponds to how often they compete. So we see the business finance people do more competitions on average than the computer science people. Consider this: the only people doing math competitions are math people. If you think about it, it’s kind of amazing how many different backgrounds are represented above. We got some cool graphics created by the students who collaborated to get the data, process it, visualize it and so on. Which universities offer courses on Data Science? There will be 26 universities in total by 2013 that offer data science courses. The balls are centered at the center of gravity of a given state, and the balls are bigger if there are more in that state. Where are data science jobs available? Observations: • We see more professional schools offering data science courses on the west coast. • It would also would be interesting to see this corrected for population size. • Only two states had no jobs. • Massachusetts #1 per capita, then Maryland Crossroads McKinsey says there will be hundreds of thousands of data science jobs in the next few years. There’s a massive demand in any case. Some of us will be part of that. It’s up to us to make sure what we’re doing is really data science, rather than validating previously held beliefs. We need to advance human knowledge if we want to take the word “scientist” seriously. How did this class empower you? You are one of the first people to take a data science class. There’s something powerful there. Thank you Rachel! Last Day of Columbia Data Science Class, What just happened? from Rachel’s perspective Recall the stated goals of this class were: • learn about what it’s like to be a data scientists • be able to do some of what a data scientist does Hey we did this! Think of all the guest lectures; they taught you a lot of what it’s like to be a data scientist, which was goal 1. Here’s what I wanted you guys to learn before the class started based on what a data scientist does, and you’ve learned a lot of that, which was goal 2: Mission accomplished! Mission accomplished? Thought experiment that I gave to myself last Spring How would you design a data science class? Comments I made to myself: • It’s not a well-defined body of knowledge, subject, no textbook! • It’s popularized and celebrated in the press and media, but there’s no “authority” to push back • I’m intellectually disturbed by idea of teaching a course when the body of knowledge is ill-defined • I didn’t know who would show up, and what their backgrounds and motivations would be • Could it become redundant with a machine learning class? My process I asked questions of myself and from other people. I gathered information, and endured existential angst about data science not being a “real thing.” I needed to give it structure. Then I started to think about it this way: while I recognize that data science has the potential to be a deep research area, it’s not there yet, and in order to actually design a class, let’s take a pragmatic approach: Recognize that data science exists. After all, there are jobs out there. I want to help students to be qualified for them. So let me teach them what it takes to get those jobs. That’s how I decided to approach it. In other words, from this perspective, data science is what data scientists do. So it’s back to the list of what data scientists do. I needed to find structure on top of that, so the structure I used as a starting point were the data scientist profiles. Data scientist profiles This was a way to think about your strengths and weaknesses, as well as a link between speakers. Note it’s easy to focus on “technical skills,” but it can also be problematic in being too skills-based, as well as being problematic because it has no scale, and no notion of expertise. On the other hand it’s good in that it allows for and captures variability among data scientists. I assigned weekly guest speakers topics related to their strengths. We held lectures, labs, and (optional) problem sessions. From this you got mad skillz: • programming in R • some python • you learned some best practices about coding From the perspective of machine learning, • you know a bunch of algorithms like linear regression, logistic regression, k-nearest neighbors, k-mean, naive Bayes, random forests, • you know what they are, what they’re used for, and how to implement them • you learned machine learning concepts like training sets, test sets, over-fitting, bias-variance tradeoff, evaluation metrics, feature selection, supervised vs. unsupervised learning • you learned about recommendation systems • you’ve entered a Kaggle competition Importantly, you now know that if there is an algorithm and model that you don’t know, you can (and will) look it up and figure it out. I’m pretty sure you’ve all improved relative to how you started. You’ve learned some data viz by taking flowing data tutorials. You’ve learned statistical inference, because we discussed • observational studies, • causal inference, and • experimental design. • We also learned some maximum likelihood topics, but I’d urge you to take more stats classes. In the realm of data engineering, • we showed you map reduce and hadoop • we worked with 30 separate shards • we used an api to get data • we spent time cleaning data • we’ve processed different kinds of data As for communication, • you wrote thoughts in response to blog posts • you observed how different data scientists communicate or present themselves, and have different styles • your final project required communicating among each other As for domain knowledge, • lots of examples were shown to you: social networks, advertising, finance, pharma, recommender systems, dallas art museum I heard people have been asking the following: why didn’t we see more data science coming from non-profits, governments, and universities? Note that data science, the term, was born in for-profits. But the truth is I’d also like to see more of that. It’s up to you guys to go get that done! How do I measure the impact of this class I’ve created? Is it possible to incubate awesome data science teams in the classroom? I might have taken you from point A to point B but you might have gone there anyway without me. There’s no counterfactual! Can we set this up as a data science problem? Can we use a causal modeling approach? This would require finding students who were more or less like you but didn’t take this class and use propensity score matching. It’s not a very well-defined experiment. But the goal is important: in industry they say you can’t learn data science in a university, that it has to be on the job. But maybe that’s wrong, and maybe this class has proved that. What has been the impact on you or to the outside world? I feel we have been contributing to the broader discourse. Does it matter if there was impact? and does it matter if it can be measured or not? Let me switch gears. What is data science again? Data science could be defined as: • A set of best practices used in tech companies, which is how I chose to design the course • A space of problems that could be solved with data • A science of data where you can think of the data itself as units The bottom two have the potential to be the basis of a rich and deep research discipline, but in many cases, the way the term is currently used is: • Pure hype But it doesn’t matter how we define it, as much as that I want for you: • to be problem solvers • to be question askers • to think about your process • to use data responsibly and make the world better, not worse. More on being problem solvers: cultivate certain habits of mind Here’s a possible list of things to strive for, taken from here: Here’s the thing. Tons of people can implement k-nearest neighbors, and many do it badly. What matters is that you cultivate the above habits, remain open to continuous learning. In education in traditional settings, we focus on answers. But what we probably should focus on is how a student behaves when they don’t know the answer. We need to have qualities that help us find the answer. Thought experiment How would you design a data science class around habits of mind rather than technical skills? How would you quantify it? How would you evaluate? What would students be able to write on their resumes? Comments from the students: • You’d need to keep making people doing stuff they don’t know how to do while keeping them excited about it. • have people do stuff in their own domains so we keep up wonderment and awe. • You’d use case studies across industries to see how things work in different contexts More on being question-askers Some suggestions on asking questions of others: • start with assumption that you’re smart • don’t assume the person you’re talking to knows more or less. You’re not trying to prove anything. • be curious like a child, not worried about appearing stupid • ask for clarification around notation or terminology • ask for clarification around process: where did this data come from? how will it be used? why is this the right data to use? who is going to do what? how will we work together? Some questions to ask yourself • does it have to be this way? • what is the problem? • how can I measure this? • what is the appropriate algorithm? • how will I evaluate this? • do I have the skills to do this? • how can I learn to do this? • who can I work with? Who can I ask? • how will it impact the real world? Data Science Processes In addition to being problem-solvers and question-askers, I mentioned that I want you to think about process. Here are a couple processes we discussed in this course: (1) Real World –> Generates Data –> –> Collect Data –> Clean, Munge (90% of your time) –> Exploratory Data Analysis –> –> Feature Selection –> –> Build Model, Build Algorithm, Visualize –> Evaluate –>Iterate–> –> Impact Real World (2) Asking questions of yourselves and others –> Identifying problems that need to be solved –> Gathering information, Measuring –> Learning to find structure in unstructured situations–> Framing Problem –> Creating Solutions –> Evaluating Thought experiment Come up with a business that improves the world and makes money and uses data Comments from the students: • autonomous self-driving cars you order with a smart phone • find all the info on people and then show them how to make it private • social network with no logs and no data retention 10 Important Data Science Ideas Of all the blog posts I wrote this semester, here’s one I think is important: 10 Important Data Science Ideas Confidence and Uncertainty Let’s talk about confidence and uncertainty from a couple perspectives. First, remember that statistical inference is extracting information from data, estimating, modeling, explaining but also quantifying uncertainty. Data Scientists could benefit from understanding this more. Learn more statistics and read Ben’s blog post on the subject. Second, we have the Dunning-Kruger Effect. Have you ever wondered why don’t people say “I don’t know” when they don’t know something? This is partly explained through an unconscious bias called the Dunning-Kruger effect. Basically, people who are bad at something have no idea that they are bad at it and overestimate their confidence. People who are super good at something underestimate their mastery of it. Actual competence may weaken self-confidence. Thought experiment Design an app to combat the dunning-kruger effect. Optimizing your life, Career Advice What are you optimizing for? What do you value? • money, need some minimum to live at the standard of living you want to, might even want a lot. • time with loved ones and friends • doing good in the world • personal fulfillment, intellectual fulfillment • goals you want to reach or achieve • being famous, respected, acknowledged • ? • some weighted function of all of the above. what are the weights? What constraints are you under? • external factors (factors outside of your control) • your resources: money, time, obligations • who you are, your education, strengths & weaknesses • things you can or cannot change about yourself There are many possible solutions that optimize what you value and take into account the constraints you’re under. So what should you do with your life? Remember that whatever you decide to do is not permanent so don’t feel too anxious about it, you can always do something else later –people change jobs all the time But on the other hand, life is short, so always try to be moving in the right direction (optimizing for what you care about). If you feel your way of thinking or perspective is somehow different than what those around you are thinking, then embrace and explore that, you might be onto something. I’m always happy to talk to you about your individual case. Next Gen Data Scientists The second blog post I think is important is this “manifesto” that I wrote: Next-Gen Data Scientists. That’s you! Go out and do awesome things, use data to solve problems, have integrity and humility. Here’s our class photo! ## Columbia Data Science course, week 12: Predictive modeling, data leakage, model evaluation This week’s guest lecturer in Rachel Schutt’s Columbia Data Science class was Claudia Perlich. Claudia has been the Chief Scientist at m6d for 3 years. Before that she was a data analytics group at the IBM center that developed Watson, the computer that won Jeopardy!, although she didn’t work on that project. Claudia got her Ph.D. in information systems at NYU and now teaches a class to business students in data science, although mostly she addresses how to assess data science work and how to manage data scientists. Claudia also holds a masters in Computer Science. Claudia is a famously successful data mining competition winner. She won the KDD Cup in 2003, 2007, 2008, and 2009, the ILP Challenge in 2005, the INFORMS Challenge in 2008, and the Kaggle HIV competition in 2010. She’s also been a data mining competition organizer, first for the INFORMS Challenge in 2009 and then for the Heritage Health Prize in 2011. Claudia claims to be retired from competition. Claudia’s advice to young people: pick your advisor first, then choose the topic. It’s important to have great chemistry with your advisor, and don’t underestimate the importance. Background Here’s what Claudia historically does with her time: • predictive modeling • data mining competitions • publications in conferences like KDD and journals • talks • patents • teaching • digging around data (her favorite part) Claudia likes to understand something about the world by looking directly at the data. Here’s Claudia’s skill set: • plenty of experience doing data stuff (15 years) • data intuition (for which one needs to get to the bottom of the data generating process) • dedication to the evaluation (one needs to cultivate a good sense of smell) • model intuition (we use models to diagnose data) Claudia also addressed being a woman. She says it works well in the data science field, where her intuition is useful and is used. She claims her nose is so well developed by now that she can smell it when something is wrong. This is not the same thing as being able to prove something algorithmically. Also, people typically remember her because she’s a woman, even when she don’t remember them. It has worked in her favor, she says, and she’s happy to admit this. But then again, she is where she is because she’s good. Someone in the class asked if papers submitted for journals and/or conferences are blind to gender. Claudia responded that it was, for some time, typically double-blind but now it’s more likely to be one-sided. And anyway there was a cool analysis that showed you can guess who wrote a paper with 80% accuracy just by knowing the citations. So making things blind doesn’t really help. More recently the names are included, and hopefully this doesn’t make things too biased. Claudia admits to being slightly biased towards institutions – certain institutions prepare better work. Skills and daily life of a Chief Data Scientist Claudia’s primary skills are as follows: • Data manipulation: unix (sed, awk, etc), Perl, SQL • Modeling: various methods (logistic regression, nearest neighbors, k-nearest neighbors, etc) • Setting things up She mentions that the methods don’t matter as much as how you’ve set it up, and how you’ve translated it into something where you can solve a question. More recently, she’s been told that at work she spends: • 40% of time as “contributor”: doing stuff directly with data • 40% of time as “ambassador”: writing stuff, giving talks, mostly external communication to represent m6d, and • 20% of time in “leadership” of her data group At IBM it was much more focused in the first category. Even so, she has a flexible schedule at m6d and is treated well. The goals of the audience She asked the class, why are you here? Do you want to: • become a data scientist? (good career choice!) • work with data scientist? • work for a data scientist? • manage a data scientist? Most people were trying their hands at the first, but we had a few in each category. She mentioned that it matters because the way she’d talk to people wanting to become a data scientist would be different from the way she’d talk to someone who wants to manage them. Her NYU class is more like how to manage one. So, for example, you need to be able to evaluate their work. It’s one thing to check a bubble sort algorithm or check whether a SQL server is working, but checking a model which purports to give the probability of people converting is different kettle of fish. For example, try to answer this: how much better can that model get if you spend another week on it? Let’s face it, quality control is hard for yourself as a data miner, so it’s definitely hard for other people. There’s no easy answer. There’s an old joke that comes to mind: What’s the difference between the scientist and a consultant? The scientists asks, how long does it take to get this right? whereas the consultant asks, how right can I get this in a week? Insights into data A student asks, how do you turn a data analysis into insights? Claudia: this is a constant point of contention. My attitude is: I like to understand something, but what I like to understand isn’t what you’d consider an insight. My message may be, hey you’ve replaced every “a” by a “0″, or, you need to change the way you collect your data. In terms of useful insight, Ori’s lecture from last week, when he talked about causality, is as close as you get. For example, decision trees you interpret, and people like them because they’re easy to interpret, but I’d ask, why does it look like it does? A slightly different data set would give you a different tree and you’d get a different conclusion. This is the illusion of understanding. I tend to be careful with delivering strong insights in that sense. For more in this vein, Claudia suggests we look at Monica Rogati‘s talk “Lies, damn lies, and the data scientist.” Data mining competitions Claudia drew a distinction between different types of data mining competitions. On the one hand you have the ”sterile” kind, where you’re given a clean, prepared data matrix, a standard error measure, and where the features are often anonymized. This is a pure machine learning problem. Examples of this first kind are: KDD Cup 2009 and 2011 (Netflix). In such competitions, your approach would emphasize algorithms and computation. The winner would probably have heavy machines and huge modeling ensembles. On the other hand, you have the ”real world” kind of data mining competition, where you’re handed raw data, which is often in lots of different tables and not easily joined, where you set up the model yourself and come up with task-specific evaluations. This kind of competition simulates real life more. Examples of this second kind are: KDD cup 2007, 2008, and 2010. If you’re competing in this kind of competition your approach would involve understanding the domain, analyzing the data, and building the model. The winner might be the person who best understands how to tailor the model to the actual question. Claudia prefers the second kind, because it’s closer to what you do in real life. In particular, the same things go right or go wrong. How to be a good modeler Claudia claims that data and domain understanding is the single most important skill you need as a data scientist. At the same time, this can’t really be taught – it can only be cultivated. A few lessons learned about data mining competitions that Claudia thinks are overlooked in academics: • Leakage: the contestants best friend and the organizers/practitioners worst nightmare. There’s always something wrong with the data, and Claudia has made an artform of figuring out how the people preparing the competition got lazy or sloppy with the data. • Adapting learning to real-life performance measures beyond standard measures like MSE, error rate, or AUC (profit?) • Feature construction/transformation: real data is rarely flat (i.e. given to you in a beautiful matrix) and good, practical solutions for this problem remains a challenge. Leakage Leakage refers to something that helps you predict something that isn’t fair. It’s a huge problem in modeling, and not just for competitions. Oftentimes it’s an artifact of reversing cause and effect. Example 1: There was a competition where you needed to predict S&P in terms of whether it would go up or go down. The winning entry had a AUC (area under the ROC curve) of 0.999 out of 1. Since stock markets are pretty close to random, either someone’s very rich or there’s something wrong. There’s something wrong. In the good old days you could win competitions this way, by finding the leakage. Example 2: Amazon case study: big spenders. The target of this competition was to predict customers who spend a lot of money among customers using past purchases. The data consisted of transaction data in different categories. But a winning model identified that “Free Shipping = True” was an excellent predictor What happened here? The point is that free shipping is an effect of big spending. But it’s not a good way to model big spending, because in particular it doesn’t work for new customers or for the future. Note: timestamps are weak here. The data that included “Free Shipping = True” was simultaneous with the sale, which is a no-no. We need to only use data from beforehand to predict the future. Example 3: Again an online retailer, this time the target is predicting customers who buy jewelry. The data consists of transactions for different categories. A very successful model simply noted that if sum(revenue) = 0, then it predicts jewelry customers very well? What happened here? The people preparing this data removed jewelry purchases, but only included people who bought something in the first place. So people who had sum(revenue) = 0 were people who only bought jewelry. The fact that you only got into the dataset if you bought something is weird: in particular, you wouldn’t be able to use this on customers before they finished their purchase. So the model wasn’t being trained on the right data to make the model useful. This is a sampling problem, and it’s common. Example 4: This happened at IBM. The target was to predict companies who would be willing to buy “websphere” solutions. The data was transaction data + crawled potential company websites. The winning model showed that if the term ”websphere” appeared on the company’s website, then they were great candidates for the product. What happened? You can’t crawl the historical web, just today’s web. Thought experiment You’re trying to study who has breast cancer. The patient ID, which seemed innocent, actually has predictive power. What happened? In the above image, red means cancerous, green means not. it’s plotted by patient ID. We see three or four distinct buckets of patient identifiers. It’s very predictive depending on the bucket. This is probably a consequence of using multiple databases, some of which correspond to sicker patients are more likely to be sick. A student suggests: for the purposes of the contest they should have renumbered the patients and randomized. Claudia: would that solve the problem? There could be other things in common as well. A student remarks: The important issue could be to see the extent to which we can figure out which dataset a given patient came from based on things besides their ID. Claudia: Think about this: what do we want these models for in the first place? How well can you predict cancer? Given a new patient, what would you do? If the new patient is in a fifth bin in terms of patient ID, then obviously don’t use the identifier model. But if it’s still in this scheme, then maybe that really is the best approach. This discussion brings us back to the fundamental problem that we need to know what the purpose of the model is and how is it going to be used in order to decide how to do it and whether it’s working. Pneumonia During an INFORMS competition on pneumonia predictions in hospital records, where the goal was to predict whether a patient has pneumonia, a logistic regression which included the number of diagnosis codes as a numeric feature (AUC of 0.80) didn’t do as well as the one which included it as a categorical feature (0.90). What’s going on? This had to do with how the person prepared the data for the competition: The diagnosis code for pneumonia was 486. So the preparer removed that (and replaced it by a “-1″) if it showed up in the record (rows are different patients, columns are different diagnoses, there are max 4 diagnoses, “-1″ means there’s nothing for that entry). Moreover, to avoid telling holes in the data, the preparer moved the other diagnoses to the left if necessary, so that only “-1″‘s were on the right. There are two problems with this: 1. If the column has only “-1″‘s, then you know it started out with only pneumonia, and 2. If the column has no “-1″‘s, you know there’s no pneumonia (unless there are actually 5 diagnoses, but that’s less common). This was enough information to win the competition. Note: winning competition on leakage is easier than building good models. But even if you don’t explicitly understand and game the leakage, your model will do it for you. Either way, leakage is a huge problem. How to avoid leakage Claudia’s advice to avoid this kind of problem: • You need a strict temporal cutoff: remove all information just prior to the event of interest (patient admission). • There has to be a timestamp on every entry and you need to keep • Removing columns asks for trouble • Removing rows can introduce inconsistencies with other tables, also causing trouble • The best practice is to start from scratch with clean, raw data after careful consideration • You need to know how the data was created! I only work with data I pulled and prepared myself (or maybe Ori). Evaluations How do I know that my model is any good? With powerful algorithms searching for patterns of models, there is a serious danger of over fitting. It’s a difficult concept, but the general idea is that “if you look hard enough you’ll find something” even if it does not generalize beyond the particular training data. To avoid overfitting, we cross-validate and we cut down on the complexity of the model to begin with. Here’s a standard picture (although keep in mind we generally work in high dimensional space and don’t have a pretty picture to look at): The picture on the left is underfit, in the middle is good, and on the right is overfit. The model you use matters when it concerns overfitting: So for the above example, unpruned decision trees are the most over fitting ones. This is a well-known problem with unpruned decision trees, which is why people use pruned decision trees. Accuracy: meh Claudia dismisses accuracy as a bad evaluation method. What’s wrong with accuracy? It’s inappropriate for regression obviously, but even for classification, if the vast majority is of binary outcomes are 1, then a stupid model can be accurate but not good (guess it’s always “1″), and a better model might have lower accuracy. Probabilities matter, not 0′s and 1′s. Nobody makes decisions on binary outcomes. I want to know the probability I have breast cancer, I don’t want to be told yes or no. It’s much more information. I care about probabilities. How to evaluate a probability model We separately evaluate the ranking and the calibration. To evaluate the ranking, we use the ROC curve and calculate the area under it, typically ranges from 0.5-1.0. This is independent of scaling and calibration. Here’s an example of how to draw an ROC curve: Sometimes to measure rankings, people draw the so-called lift curve: The key here is that the lift is calculated with respect to a baseline. You draw it at a given point, say 10%, by imagining that 10% of people are shown ads, and seeing how many people click versus if you randomly showed 10% of people ads. A lift of 3 means it’s 3 times better. How do you measure calibration? Are the probabilities accurate? If the model says probability of 0.57 that I have cancer, how do I know if it’s really 0.57? We can’t measure this directly. We can only bucket those predictions and then aggregately compare those in that prediction bucket (say 0.50-0.55) to the actual results for that bucket. For example, here’s what you get when your model is an unpruned decision tree, where the blue diamonds are buckets: A good model would show buckets right along the x=y curve, but here we’re seeing that the predictions were much more extreme than the actual probabilities. Why does this pattern happen for decision trees? Claudia says that this is because trees optimize purity: it seeks out pockets that have only positives or negatives. Therefore its predictions are more extreme than reality. This is generally true about decision trees: they do not generally perform well with respect to calibration. Logistic regression looks better when you test calibration, which is typical: Takeaways: • Accuracy is almost never the right evaluation metric. • Probabilities, not binary outcomes. • Separate ranking from calibration. • Ranking you can measure with nice pictures: ROC, lift • Calibration is measured indirectly through binning. • Different models are better than others when it comes to calibration. • Calibration is sensitive to outliers. • Measure what you want to be good at. • Have a good baseline. Choosing an algorithm This is not a trivial question and in particular small tests may steer you wrong, because as you increase the sample size the best algorithm might vary: often decision trees perform very well but only if there’s enough data. In general you need to choose your algorithm depending on the size and nature of your dataset and you need to choose your evaluation method based partly on your data and partly on what you wish to be good at. Sum of squared error is maximum likelihood loss function if your data can be assumed to be normal, but if you want to estimate the median, then use absolute errors. If you want to estimate a quantile, then minimize the weighted absolute error. We worked on predicting the number of ratings of a movie will get in the next year, and we assumed a poisson distributions. In this case our evaluation method doesn’t involve minimizing the sum of squared errors, but rather something else which we found in the literature specific to the Poisson distribution, which depends on the single parameter $\lambda$: Charity direct mail campaign Let’s put some of this together. Say we want to raise money for a charity. If we send a letter to every person in the mailing list we raise about$9000. We’d like to save money and only send money to people who are likely to give – only about 5% of people generally give. How can we do that?

If we use a (somewhat pruned, as is standard) decision tree, we get $0 profit: it never finds a leaf with majority positives. If we use a neural network we still make only$7500, even if we only send a letter in the case where we expect the return to be higher than the cost.

This looks unworkable. But if you model is better, it’s not. A person makes two decisions here. First, they decide whether or not to give, then they decide how much to give. Let’s model those two decisions separately, using:

$E(\|person) = P(response = 'yes'| person) \cdot E(\|response = 'yes', person).$

Note we need the first model to be well-calibrated because we really care about the number, not just the ranking. So we will try logistic regression for first half. For the second part, we train with special examples where there are donations.

Altogether this decomposed model makes a profit of $15,000. The decomposition made it easier for the model to pick up the signals. Note that with infinite data, all would have been good, and we wouldn’t have needed to decompose. But you work with what you got. Moreover, you are multiplying errors above, which could be a problem if you have a reason to believe that those errors are correlated. Parting thoughts We are not meant to understand data. Data are outside of our sensory systems and there are very few people who have a near-sensory connection to numbers. We are instead meant to understand language. We are not mean to understand uncertainty: we have all kinds of biases that prevent this from happening and are well-documented. Modeling people in the future is intrinsically harder than figuring out how to label things that have already happened. Even so we do our best, and this is through careful data generation, careful consideration of what our problem is, making sure we model it with data close to how it will be used, making sure we are optimizing to what we actually desire, and doing our homework in learning which algorithms fit which tasks. ## O’Reilly book deal signed for “Doing Data Science” I’m very happy to say I just signed a book contract with my co-author, Rachel Schutt, to publish a book with O’Reilly called Doing Data Science. The book will be based on the class Rachel is giving this semester at Columbia which I’ve been blogging about here. For those of you who’ve been reading along for free as I’ve been blogging it, there might not be a huge incentive to buy it, but I can promise you more and better math, more explicit usable formulas, some sample code, and an overall better and more thought-out narrative. It’s supposed to be published in May with a possible early release coming up at the end of February, in time for the O’Reilly Strata Santa Clara conference, where Rachel will be speaking about it and about other stuff curriculum related. Hopefully people will pick it up in time to teach their data science courses in Fall 2013. Speaking of Rachel, she’s also been selected to give a TedXWomen talk at Barnard on December 1st, which is super exciting. She’s talking about advocating for the social good using data. Unfortunately the event is invitation-only, otherwise I’d encourage you all to go and hear her words of wisdom. Update: word on the street is that it will be video-taped. ## Columbia Data Science course, week 11: Estimating causal effects The week in Rachel Schutt’s Data Science course at Columbia we had Ori Stitelman, a data scientist at Media6Degrees. We also learned last night of a new Columbia course: STAT 4249 Applied Data Science, taught by Rachel Schutt and Ian Langmore. More information can be found here. Ori’s background Ori got his Ph.D. in Biostatistics from UC Berkeley after working at a litigation consulting firm. He credits that job with allowing him to understand data through exposure to tons of different data sets; since his job involved creating stories out of data to let experts testify at trials, e.g. for asbestos. In this way Ori developed his data intuition. Ori worries that people ignore this necessary data intuition when they shove data into various algorithms. He thinks that when their method converges, they are convinced the results are therefore meaningful, but he’s here today to explain that we should be more thoughtful than that. It’s very important when estimating causal parameters, Ori says, to understand the data-generating distributions and that involves gaining subject matter knowledge that allows you to understand if you necessary assumptions are plausible. Ori says the first step in a data analysis should always be to take a step back and figure out what you want to know, write that down, and then find and use the tools you’ve learned to answer those directly. Later of course you have to decide how close you came to answering your original questions. Thought Experiment Ori asks, how do you know if your data may be used to answer your question of interest? Sometimes people think that because they have data on a subject matter then you can answer any question. Students had some ideas: • You need coverage of your parameter space. For example, if you’re studying the relationship between household income and holidays but your data is from poor households, then you can’t extrapolate to rich people. (Ori: but you could ask a different question) • Causal inference with no timestamps won’t work. • You have to keep in mind what happened when the data was collected and how that process affected the data itself • Make sure you have the base case: compared to what? If you want to know how politicians are affected by lobbyists money you need to see how they behave in the presence of money and in the presence of no money. People often forget the latter. • Sometimes you’re trying to measure weekly effects but you only have monthly data. You end up using proxies. Ori: but it’s still good practice to ask the precise question that you want, then come back and see if you’ve answered it at the end. Sometimes you can even do a separate evaluation to see if something is a good proxy. • Signal to noise ratio is something to worry about too: as you have more data, you can more precisely estimate a parameter. You’d think 10 observations about purchase behavior is not enough, but as you get more and more examples you can answer more difficult questions. Ori explains confounders with a dating example Frank has an important decision to make. He’s perusing a dating website and comes upon a very desirable woman – he wants her number. What should he write in his email to her? Should he tell her she is beautiful? How do you answer that with data? You could have him select a bunch of beautiful women and half the time chosen at random, tell them they’re beautiful. Being random allows us to assume that the two groups have similar distributions of various features (not that’s an assumption). Our real goal is to understand the future under two alternative realities, the treated and the untreated. When we randomize we are making the assumption that the treated and untreated populations are alike. OK Cupid looked at this and concluded: But note: • It could say more about the person who says “beautiful” than the word itself. Maybe they are otherwise ridiculous and overly sappy? • The recipients of emails containing the word “beautiful” might be special: for example, they might get tons of email, which would make it less likely for Frank to get any response at all. • For that matter, people may be describing themselves as beautiful. Ori points out that this fact, that she’s beautiful, affects two separate things: 1. whether Frank uses the word “beautiful” or not in his email, and 2. the outcome (i.e. whether Frank gets the phone number). For this reason, the fact that she’s beautiful qualifies as a confounder. The treatment is Frank writing “beautiful” in his email. Causal graphs Denote by $W$ the list of all potential confounders. Note it’s an assumption that we’ve got all of them (and recall how unreasonable this seems to be in epidemiology research). Denote by $A$ the treatment (so, Frank using the word “beautiful” in the email). We usually assume this to have a binary (0/1) outcome. Denote by $Y$ the binary (0/1) outcome (Frank getting the number). We are forming the following causal graph: In a causal graph, each arrow means that the ancestor is a cause of the descendent, where ancestor is the node the arrow is coming out of and the descendent is the node the arrow is going into (see this book for more). In our example with Frank, the arrow from beauty means that the woman being beautiful is a cause of Frank writing “beautiful” in the message. Both the man writing “beautiful” and and the woman being beautiful are direct causes of her probability to respond to the message. Setting the problem up formally The building blocks in understanding the above causal graph are: 1. Ask question of interest. 2. Make causal assumptions (denote these by $P$). 3. Translate question into a formal quantity (denote this by $\Psi(P)$). 4. Estimate quantity (denote this by $\Psi(P_n)$). We need domain knowledge in general to do this. We also have to take a look at the data before setting this up, for example to make sure we may make the Positivity Assumption. We need treatment (i.e. data) in all strata of things we adjust for. So if think gender is a confounder, we need to make sure we have data on women and on men. If we also adjust for age, we need data in all of the resulting bins. Asking causal questions What is the effect of ___ on ___? This is the natural form of a causal question. Here are some examples: 1. What is the effect of advertising on customer behavior? 2. What is the effect of beauty on getting a phone number? 3. What is the effect of censoring on outcome? (censoring is when people drop out of a study) 4. What is the effect of drug on time until viral failure?, and the general case 5. What is the effect of treatment on outcome? Look, estimating causal parameters is hard. In fact the effectiveness of advertising is almost always ignored because it’s so hard to measure. Typically people choose metrics of success that are easy to estimate but don’t measure what they want! Everyone makes decision based on them anyway because it’s easier. This results in people being rewarded for finding people online who would have converted anyway. Accounting for the effect of interventions Thinking about that, we should be concerned with the effect of interventions. What’s a model that can help us understand that effect? A common approach is the (randomized) A/B test, which involves the assumption that two populations are equivalent. As long as that assumption is pretty good, which it usually is with enough data, then this is kind of the gold standard. But A/B tests are not always possible (or they are too expensive to be plausible). Often we need to instead estimate the effects in the natural environment, but then the problem is the guys in different groups are actually quite different from each other. So, for example, you might find you showed ads to more people who are hot for the product anyway; it wouldn’t make sense to test the ad that way without adjustment. The game is then defined: how do we adjust for this? The ideal case Similar to how we did this last week, we pretend for now that we have a “full” data set, which is to say we have god-like powers and we know what happened under treatment as well as what would have happened if we had not treated, as well as vice-versa, for every agent in the test. Denote this full data set by $X:$ $X = (W, A, Y^*(1), Y^*(0)),$ where • $W$ denotes the baseline variables (attributes of the agent) as above, • $A$ denotes the binary treatment as above, • $Y^*(1)$ denotes the binary outcome if treated, and • $Y^*(0)$ denotes the binary outcome if untreated. As a baseline check: if we observed this full data structure how would we measure the effect of A on Y? In that case we’d be all-powerful and we would just calculate: $E(Y^*(1)) - E(Y^*(0)).$ Note that, since $Y^*(0)$ and $Y^*(1)$ are binary, the expected value $E(Y^*(0))$ is just the probability of a positive outcome if untreated. So in the case of advertising, the above is the conversion rate change when you show someone an ad. You could also take the ratio of the two quantities: $E(Y^*(1))/E(Y^*(0)).$ This would be calculating how much more likely someone is to convert if they see an ad. Note these are outcomes you can really do stuff with. If you know people convert at 30% versus 10% in the presence of an ad, that’s real information. Similarly if they convert 3 times more often. In reality people use silly stuff like log odds ratios, which nobody understands or can interpret meaningfully. The ideal case with functions In reality we don’t have god-like powers, and we have to make do. We will make a bunch of assumptions. First off, denote by $U$ exogenous variables, i.e. stuff we’re ignoring. Assume there are functions $f_1, f_2,$ and $f_3$ so that: • $W = f_1(U_W),$ i.e. the attributes $W$ are just functions of some exogenous variables, • $A = f_2(W, U_A),$ i.e. the treatment depends in a nice way on some exogenous variables as well the attributes we know about living in $W$, and • $Y = f_3(A, W, U_Y),$ i.e. the outcome is just a function of the treatment, the attributes, and some exogenous variables. Note the various $U$‘s could contain confounders in the above notation. That’s gonna change. But we want to intervene on this causal graph as though it’s the intervention we actually want to make. i.e. what’s the effect of treatment $A$ on outcome $Y$? Let’s look at this from the point of view of the joint distribution $P(W, A, Y) = P(W)P(A|W)P(Y|A,W).$ These terms correspond to the following in our example: 1. the probability of a woman being beautiful, 2. the probability that Frank writes and email to a her saying that she’s beautiful, and 3. the probability that Frank gets her phone number. What we really care about though is the distribution under intervention: $P_a = P(W) P(Y_a| W),$ i.e. the probability knowing someone either got treated or not. To answer our question, we manipulate the value of $A,$ first setting it to 1 and doing the calculation, then setting it to 0 and redoing the calculation. Assumptions We are making a “Consistency Assumption / SUTVA” which can be expressed like this: We have also assumed that we have no unmeasured confounders, which can be expressed thus: We are also assuming positivity, which we discussed above. Down to brass tacks We only have half the information we need. We need to somehow map the stuff we have to the full data set as defined above. We make use of the following identity: Recall we want to estimate $\Psi(P) = E(Y^*(1))/E(Y^*(0)),$ which by the above can be rewritten $E_W(E(Y|A=1, W))/ E_W(E(Y|A=0, W)).$ We’re going to discuss three methods to estimate this quantity, namely: 1. MLE-based substitution estimator (MLE), 2. Inverse probability estimators (IPTW), 3. Double robust estimating equations (A-IPTW) For the above models, it’s useful to think of there being two machines, called $g$ and $Q$, which generate estimates of the probability of the treatment knowing the attributes (that’s machine $g$) and the probability of the outcome knowing the treatment and the attributes (machine $Q$). IPTW In this method, which is also called importance sampling, we weight individuals that are unlikely to be shown an ad more than those likely. In other words, we up-sample in order to generate the distribution, to get the estimation of the actual effect. To make sense of this, imagine that you’re doing a survey of people to see how they’ll vote, but you happen to do it at a soccer game where you know there are more young people than elderly people. You might want to up-sample the elderly population to make your estimate. This method can be unstable if there are really small sub-populations that you’re up-sampling, since you’re essentially multiplying by a reciprocal. The formula in IPTW looks like this: Note the formula depends on the $g$ machine, i.e. the machine that estimates the treatment probability based on attributes. The problem is that people get the $g$ machine wrong all the time, which makes this method fail. In words, when $a=1$ we are taking the sum of terms whose numerators are zero unless we have a treated, positive outcome, and we’re weighting them in the denominator by the probability of getting treated so each “population” has the same representation. We do the same for $a=0$ and take the difference. MLE This method is based on the $Q$ machine, which as you recall estimates the probability of a positive outcome given the attributes and the treatment, so the$latex P(Y|A,W)$values. This method is straight-forward: shove everyone in the machine and predict how the outcome would look under both treatment and non-treatment conditions, and take difference. Note we don’t know anything about the underlying machine$latex Q$. It could be a logistic regression. Get ready to get worried: A-IPTW What if our machines are broken? That’s when we bring in the big guns: double robust estimators. They adjust for confounding through the two machines we have on hand, $Q$ and $g,$ and one machine augments the other depending on how well it works. Here’s the functional form written in two ways to illustrate the hedge: and Note: you are still screwed if both machines are broken. In some sense with a double robust estimator you’re hedging your bet. “I’m glad you’re worried because I’m worried too.” – Ori Simulate and test I’ve shown you 3 distinct methods that estimate effects in observational studies. But they often come up with different answers. We set up huge simulation studies with known functions, i.e. where we know the functional relationships between everything, and then tried to infer those using the above three methods as well as a fourth method called TMLE (targeted maximal likelihood estimation). As a side note, Ori encourages everyone to simulate data. We wanted to know, which methods fail with respect to the assumptions? How well do the estimates work? We started to see that IPTW performs very badly when you’re adjusting by very small thing. For example we found that the probability of someone getting sick is 132. That’s not between 0 and 1, which is not good. But people use these methods all the time. Moreover, as things get more complicated with lots of nodes in our causal graph, calculating stuff over long periods of time, populations get sparser and sparser and it has an increasingly bad effect when you’re using IPTW. In certain situations your data is just not going to give you a sufficiently good answer. Causal analysis in online display advertising An overview of the process: 1. We observe people taking actions (clicks, visits to websites, purchases, etc.). 2. We use this observed data to build list of “prospects” (people with a liking for the brand). 3. We subsequently observe same user during over the next few days. 4. The user visits a site where a display ad spot exists and bid requests are made. 5. An auction is held for display spot. 6. If the auction is won, we display the ad. 7. We observe the user’s actions after displaying the ad. But here’s the problem: we’ve instituted confounders – if you find people who convert highly they think you’ve done a good job. In other words, we are looking at the treated without looking at the untreated. We’d like to ask the question, what’s the effect of display advertising on customer conversion? As a practical concern, people don’t like to spend money on blank ads. So A/B tests are a hard sell. We performed some what-if analysis stipulated on the assumption that the group of users that sees ad is different. Our process was as follows: 1. Select prospects that we got a bid request for on day 0 2. Observe if they were treated on day 1. For those treated set $A=1$ and those not treated set $A=0.$ collect attributes $W.$ 3. Create outcome window to be the next five days following treatment; observe if outcome event occurs (visit to the website whose ad was shown). 4. Estimate model parameters using the methods previously described (our three methods plus TMLE). Here are some results: Note results vary depending on the method. And there’s no way to know which method is working the best. Moreover, this is when we’ve capped the size of the correction in the IPTW methods. If we don’t then we see ridiculous results: ## Columbia Data Science course, week 10: Observational studies, confounders, epidemiology This week our guest lecturer in the Columbia Data Science class was David Madigan, Professor and Chair of Statistics at Columbia. He received a bachelors degree in Mathematical Sciences and a Ph.D. in Statistics, both from Trinity College Dublin. He has previously worked for AT&T Inc., Soliloquy Inc., the University of Washington, Rutgers University, and SkillSoft, Inc. He has over 100 publications in such areas as Bayesian statistics, text mining, Monte Carlo methods, pharmacovigilance and probabilistic graphical models. So Madigan is an esteemed guest, but I like to call him an “apocalyptic leprechaun”, for reasons which you will know by the end of this post. He’s okay with that nickname, I asked his permission. Madigan came to talk to us about observation studies, of central importance in data science. He started us out with this: Thought Experiment We now have detailed, longitudinal medical data on tens of millions of patients. What can we do with it? To be more precise, we have tons of phenomenological data: this is individual, patient-level medical record data. The largest of the databases has records on 80 million people: every prescription drug, every condition ever diagnosed, every hospital or doctor’s visit, every lab result, procedures, all timestamped. But we still do things like we did in the Middle Ages; the vast majority of diagnosis and treatment is done in a doctor’s brain. Can we do better? Can you harness these data to do a better job delivering medical care? Students responded: 1) There was a prize offered on Kaggle, called “Improve Healthcare, Win$3,000,000.” predicting who is going to go to the hospital next year. Doesn’t that give us some idea of what we can do?

Madigan: keep in mind that they’ve coarsened the data for proprietary reasons. Hugely important clinical problem, especially as a healthcare insurer. Can you intervene to avoid hospitalizations?

2) We’ve talked a lot about the ethical uses of data science in this class. It seems to me that there are a lot of sticky ethical issues surrounding this 80 million person medical record dataset.

Madigan: Agreed! What nefarious things could we do with this data? We could gouge sick people with huge premiums, or we could drop sick people from insurance altogether. It’s a question of what, as a society, we want to do.

What is modern academic statistics?

Madigan showed us Drew Conway’s Venn Diagram that we’d seen in week 1:

Madigan positioned the modern world of the statistician in the green and purple areas.

It used to be the case, say 20 years ago, according to Madigan, that academic statistician would either sit in their offices proving theorems with no data in sight (they wouldn’t even know how to run a t-test) or sit around in their offices and dream up a new test, or a new way of dealing with missing data, or something like that, and then they’d look around for a dataset to whack with their new method. In either case, the work of an academic statistician required no domain expertise.

Nowadays things are different. The top stats journals are more deep in terms of application areas, the papers involve deep collaborations with people in social sciences or other applied sciences. Madigan is setting an example tonight by engaging with the medical community.

Madigan went on to make a point about the modern machine learning community, which he is or was part of: it’s a newish academic field, with conferences and journals, etc., but is characterized by what stats was 20 years ago: invent a method, try it on datasets. In terms of domain expertise engagement, it’s a step backwards instead of forwards.

Comments like the above make me love Madigan.

Very few academic statisticians have serious hacking skills, with Mark Hansen being an unusual counterexample. But if all three is what’s required to be called data science, then I’m all for data science, says Madigan.

Madigan’s timeline

Madigan went to college in 1980, specialized on day 1 on math for five years. In final year, he took a bunch of stats courses, and learned a bunch about computers: pascal, OS, compilers, AI, database theory, and rudimentary computing skills. Then came 6 years in industry, working at an insurance company and a software company where he specialized in expert systems.

It was a mainframe environment, and he wrote code to price insurance policies using what would now be described as scripting languages. He also learned about graphics by creating a graphic representation of a water treatment system. He learned about controlling graphics cards on PC’s, but he still didn’t know about data.

Then he got a Ph.D. and went into academia. That’s when machine learning and data mining started, which he fell in love with: he was Program Chair of the KDD conference, among other things, before he got disenchanted. He learned C and java, R and S+. But he still wasn’t really working with data yet.

He claims he was still a typical academic statistician: he had computing skills but no idea how to work with a large scale medical database, 50 different tables of data scattered across different databases with different formats.

In 2000 he worked for AT&T labs. It was an “extreme academic environment”, and he learned perl and did lots of stuff like web scraping. He also learned awk and basic unix skills.

It was life altering and it changed everything: having tools to deal with real data rocks! It could just as well have been python. The point is that if you don’t have the tools you’re handicapped. Armed with these tools he is afraid of nothing in terms of tackling a data problem.

In Madigan’s opinion, statisticians should not be allowed out of school unless they know these tools.

He then went to a internet startup where he and his team built a system to deliver real-time graphics on consumer activity.

Since then he’s been working in big medical data stuff. He’s testified in trials related to medical trials, which was eye-opening for him in terms of explaining what you’ve done: “If you’re gonna explain logistical regression to a jury, it’s a different kind of a challenge than me standing here tonight.” He claims that super simple graphics help.

Carrotsearch

As an aside he suggests we go to this website, called carrotsearch, because there’s a cool demo on it.

What is an observational study?

Madigan defines it for us:

An observational study is an empirical study in which the objective is to elucidate cause-and-effect relationships in which it is not feasible to use controlled experimentation.

In tonight’s context, it will involve patients as they undergo routine medical care. We contrast this with designed experiment, which is pretty rare. In fact, Madigan contends that most data science activity revolves around observational data. Exceptions are A/B tests. Most of the time, the data you have is what you get. You don’t get to replay a day on the market where Romney won the presidency, for example.

Observational studies are done in contexts in which you can’t do experiments, and they are mostly intended to elucidate cause-and-effect. Sometimes you don’t care about cause-and-effect, you just want to build predictive models. Madigan claims there are many core issues in common with the two.

Here are some examples of tests you can’t run as designed studies, for ethical reasons:

• smoking and heart disease (you can’t randomly assign someone to smoke)
• vitamin C and cancer survival
• DES and vaginal cancer
• aspirin and mortality
• cocaine and birthweight
• diet and mortality

Pitfall #1: confounders

There are all kinds of pitfalls with observational studies.

For example, look at this graph, where you’re finding a best fit line to describe whether taking higher doses of the “bad drug” is correlated to higher probability of a heart attack:

It looks like, from this vantage point, the more drug you take the fewer heart attacks you have. But there are two clusters, and if you know more about those two clusters, you find the opposite conclusion:

Note this picture was rigged it so the issue is obvious. This is an example of a “confounder.” In other words, the aspirin-taking or non-aspirin-taking of the people in the study wasn’t randomly distributed among the people, and it made a huge difference.

It’s a general problem with regression models on observational data. You have no idea what’s going on.

Madigan: “It’s the wild west out there.”

Wait, and it gets worse. It could be the case that within each group there males and females and if you partition by those you see that the more drugs they take the better again. Since a given person either is male or female, and either takes aspirin or doesn’t, this kind of thing really matters.

This illustrates the fundamental problem in observational studies, which is sometimes called Simpson’s Paradox.

[Remark from someone in the class: if you think of the original line as a predictive model, it's actually still the best model you can obtain knowing nothing more about the aspirin-taking habits or genders of the patients involved. The issue here is really that you're trying to assign causality.]

The medical literature and observational studies

As we may not be surprised to hear, medical journals are full of observational studies. The results of these studies have a profound effect on medical practice, on what doctors prescribe, and on what regulators do.

For example, in this paper, entitled “Oral bisphosphonates and risk of cancer of oesophagus, stomach, and colorectum: case-control analysis within a UK primary care cohort,” Madigan report that we see the very same kind of confounding problem as in the above example with aspirin. The conclusion of the paper is that the risk of cancer increased with 10 or more prescriptions of oral bisphosphonates.

It was published on the front page of new york times, the study was done by a group with no apparent conflict of interest and the drugs are taken by millions of people. But the results were wrong.

There are thousands of examples of this, it’s a major problem and people don’t even get that it’s a problem.

Randomized clinical trials

One possible way to avoid this problem is randomized studies. The good news is that randomization works really well: because you’re flipping coins, all other factors that might be confounders (current or former smoker, say) are more or less removed, because I can guarantee that smokers will be fairly evenly distributed between the two groups if there are enough people in the study.

The truly brilliant thing about randomization is that randomization matches well on the possible confounders you thought of, but will also give you balance on the 50 million things you didn’t think of.

So, although you can algorithmically find a better split for the ones you thought of, that quite possible wouldn’t do as well on the other things. That’s why we really do it randomly, because it does quite well on things you think of and things you don’t.

But there’s bad news for randomized clinical trials as well. First off, it’s only ethically feasible if there’s something called clinical equipoise, which means the medical community really doesn’t know which treatment is better. If you know have reason to think treating someone with a drug will be better for them than giving them nothing, you can’t randomly not give people the drug.

The other problem is that they are expensive and cumbersome. It takes a long time and lots of people to make a randomized clinical trial work.

In spite of the problems, randomized clinical trials are the gold standard for elucidating cause-and-effect relationships.

Rubin causal model

The Rubin causal model is a mathematical framework for understanding what information we know and don’t know in observational studies.

It’s meant to investigate the confusion when someone says something like “I got lung cancer because I smoked”. Is that true? If so, you’d have to be able to support the statement, “If I hadn’t smoked I wouldn’t have gotten lung cancer,” but nobody knows that for sure.

Define:

• $Z_i$ to be the treatment applied to unit $i$ (0 = control, 1= treatment),
• $Y_i(1)$ to be the response for unit $i$ if $Z_i = 1$,
• $Y_i(0)$ to be the response for unit $i$ if $Z_i = 0$.

Then the unit level causal effect is $Y_i(1)-Y_i(0)$, but we only see one of $Y_i(0)$ and $Y_i(1).$

Example: $Z_i$ is 1 if I smoked, 0 if I didn’t (I am the unit). $Y_i(1)$ is 1 or 0 if I got cancer and I smoked, and $Y_i(0)$ is 1 or 0 depending on whether I got cancer while not smoking. The overall causal effect on me is the difference $Y_i(1)-Y_i(0).$ This is equal to 1 if I got really got cancer because I smoked, it’s 0 if I got cancer (or didn’t) independent of smoking, and it’s -1 if I avoided cancer by smoking. But I’ll never know my actual value since I only know one term out of the two.

Of course, on a population level we do know how to infer that there are quite a few “1″‘s among the population, but we will never be able to assign a given individual that number.

This is sometimes called the fundamental problem of causal inference.

Confounding and Causality

Let’s say we have a population of 100 people that takes some drug, and we screen them for cancer. Say 30 out of them get cancer, which gives them a cancer rate of 0.30. We want to ask the question, did the drug cause the cancer?

To answer that, we’d have to know what would’ve happened if they hadn’t taken the drug. Let’s play God and stipulate that, had they not taken the drug, we would have seen 20 get cancer, so a rate of 0.20. We typically say the causal effect is the ration of these two numbers (i.e. the increased risk of cancer), so 1.5.

But we don’t have God’s knowledge, so instead we choose another population to compare this one to, and we see whether they get cancer or not, whilst not taking the drug. Say they have a natural cancer rate of 0.10. Then we would conclude, using them as a proxy, that the increased cancer rate is the ratio 0.30 to 0.10, so 3. This is of course wrong, but the problem is that the two populations have some underlying differences that we don’t account for.

If these were the “same people”, down to the chemical makeup of each other molecules, this “by proxy” calculation would work of course.

The field of epidemiology attempts to adjust for potential confounders. The bad news is that it doesn’t work very well. One reason is that they heavily rely on stratification, which means partitioning the cases into subcases and looking at those. But there’s a problem here too.

Stratification can introduce confounding.

The following picture illustrates how stratification could make the underlying estimates of the causal effects go from good to bad:

In the top box, the values of b and c are equal, so our causal effect estimate is correct. However, when you break it down by male and female, you get worse estimates of causal effects.

The point is, stratification doesn’t just solve problems. There are no guarantees your estimates will be better if you stratify and all bets are off.

What do people do about confounding things in practice?

In spite of the above, experts in this field essentially use stratification as a major method to working through studies. They deal with confounding variables by essentially stratifying with respect to them. So if taking aspirin is believed to be a potential confounding factor, they stratify with respect to it.

For example, with this study, which studied the risk of venous thromboembolism from the use of certain kinds of oral contraceptives, the researchers chose certain confounders to worry about and concluded the following:

After adjustment for length of use, users of oral contraceptives were at least twice the risk of clotting compared with user of other kinds of oral contraceptives.

This report was featured on ABC, and it was a big hoo-ha.

Madigan asks: wouldn’t you worry about confounding issues like aspirin or something? How do you choose which confounders to worry about? Wouldn’t you worry that the physicians who are prescribing them are different in how they prescribe? For example, might they give the newer one to people at higher risk of clotting?

Another study came out about this same question and came to a different conclusion, using different confounders. They adjusted for a history of clots, which makes sense when you think about it.

This is an illustration of how you sometimes forget to adjust for things, and the outputs can then be misleading.

What’s really going on here though is that it’s totally ad hoc, hit or miss methodology.

Another example is a study on oral bisphosphonates, where they adjusted for smoking, alcohol, and BMI. But why did they choose those variables?

There are hundreds of examples where two teams made radically different choices on parallel studies. We tested this by giving a bunch of epidemiologists the job to design 5 studies at a high level. There was zero consistency. And an addition problem is that luminaries of the field hear this and say: yeah yeah yeah but I would know the right way to do it.

Is there a better way?

Madigan and his co-authors examined 50 studies, each of which corresponds to a drug and outcome pair, e.g. antibiotics with GI bleeding.

They ran about 5,000 analyses for every pair. Namely, they ran every epistudy imaginable on, and they did this all on 9 different databases.

For example, they looked at ACE inhibitors (the drug) and swelling of the heart (outcome). They ran the same analysis on the 9 different standard databases, the smallest of which has records of 4,000,000 patients, and the largest of which has records of 80,000,000 patients.

In this one case, for one database the drug triples the risk of heart swelling, but for another database it seems to have a 6-fold increase of risk. That’s one of the best examples, though, because at least it’s always bad news – it’s consistent.

On the other hand, for 20 of the 50 pairs, you can go from statistically significant in one direction (bad or good) to the other direction depending on the database you pick. In other words, you can get whatever you want. Here’s a picture, where the heart swelling example is at the top:

Note: the choice of database is never discussed in any of these published epidemiology papers.

Next they did an even more extensive test, where they essentially tried everything. In other words, every time there was a decision to be made, they did it both ways. The kinds of decisions they tweaker were of the following types: which database you tested on, the confounders you accounted for, the window of time you care about examining (spoze they have a heart attack a week after taking the drug, is it counted? 6 months?)

What they saw was that almost all the studies can get either side depending on the choices.

Final example, back to oral bisphosphonates. A certain study concluded that it causes esophageal cancer, but two weeks later JAMA published a paper on same issue which concluded it is not associated to elevated risk of esophageal cancer. And they were even using the same database. This is not so surprising now for us.

OMOP Research Experiment

Here’s the thing. Billions upon billions of dollars are spent doing these studies. We should really know if they work. People’s lives depend on it.

Madigan told us about his “OMOP 2010.2011 Research Experiment”

They took 10 large medical databases, consisting of a mixture of claims from insurance companies and EHR (electronic health records), covering records of 200 million people in all. This is big data unless you talk to an astronomer.

They mapped the data to a common data model and then they implemented every method used in observational studies in healthcare. Altogether they covered 14 commonly used epidemiology designs adapted for longitudinal data. They automated everything in sight. Moreover, there were about 5000 different “settings” on the 14 methods.

The idea was to see how well the current methods do on predicting things we actually already know.

To locate things they know, they took 10 old drug classes: ACE inhibitors, beta blockers, warfarin, etc., and 10 outcomes of interest: renal failure, hospitalization, bleeding, etc.

For some of these the results are known. So for example, warfarin is a blood thinner and definitely causes bleeding. There were 9 such known bad effects.

There were also 44 known “negative” cases, where we are super confident there’s just no harm in taking these drugs, at least for these outcomes.

The basic experiment was this: run 5000 commonly used epidemiological analyses using all 10 databases. How well do they do at discriminating between reds and blues?

This is kind of like a spam filter test. We have training emails that are known spam, and you want to know how well the model does at detecting spam when it comes through.

Each of the models output the same thing: a relative risk (causal effect estimate) and an error.

This was an attempt to empirically evaluate how well does epidemiology work, kind of the quantitative version of John Ioannidis’s work. we did the quantitative thing to show he’s right.

Why hasn’t this been done before? There’s conflict of interest for epidemiology – why would they want to prove their methods don’t work? Also, it’s expensive, it cost $25 million dollars (of course that pales in comparison to the money being put into these studies). They bought all the data, made the methods work automatically, and did a bunch of calculations in the Amazon cloud. The code is open source. In the second version, we zeroed in on 4 particular outcomes. Here’s the$25,000,000 ROC curve:

To understand this graph, we need to define a threshold, which we can start with at 2. This means that if the relative risk is estimated to be above 2, we call it a “bad effect”, otherwise call it a “good effect.” The choice of threshold will of course matter.

If it’s high, say 10, then you’ll never see a 10, so everything will be considered a good effect. Moreover these are old drugs and it wouldn’t be on the market. This means your sensitivity will be low, and you won’t find any real problem. That’s bad! You should find, for example, that warfarin causes bleeding.

There’s of course good news too, with low sensitivity, namely a zero false-positive rate.

What if you set the threshold really low, at -10? Then everything’s bad, and you have a 100% sensitivity but very high false positive rate.

As you vary the threshold from very low to very high, you sweep out a curve in terms of sensitivity and false-positive rate, and that’s the curve we see above. There is a threshold (say 1.8) for which your false positive rate is 30% and your sensitivity is 50%.

This graph is seriously problematic if you’re the FDA. A 30% false-positive rate is out of control. This curve isn’t good.

The overall “goodness” of such a curve is usually measured as the area under the curve: you want it to be one, and if your curve lies on diagonal the area is 0.5. This is tantamount to guessing randomly. So if your area under the curve is less than 0.5, it means your model is perverse.

The area above is 0.64. Moreover, of the 5000 analysis we ran, this is the single best analysis.

But note: this is the best if I can only use the same method for everything. In that case this is as good as it gets, and it’s not that much better than guessing.

But no epidemiology would do that!

So what they did next was to specialize the analysis to the database and the outcome. And they got better results: for the medicare database, and for acute kidney injury, their optimal model gives them an AUC of 0.92. They can achieve 80% sensitivity with a 10% false positive rate.

They did this using a cross-validation method. Different databases have different methods attached to them. One winning method is called “OS”, which compares within a given patient’s history (so compares times when patient was on drugs versus when they weren’t). This is not widely used now.

The epidemiologists in general don’t believe the results of this study.

If you go to http://elmo/omop.org, you can see the AUM for a given database and a given method.

Note the data we used was up to mid-2010. To update this you’d have to get latest version of database, and rerun the analysis. Things might have changed.

Moreover, an outcome for which nobody has any idea on what drugs cause what outcomes you’re in trouble. This only applies to when we have things to train on where we know the outcome pretty well.

Parting remarks

Keep in mind confidence intervals only account for sampling variability. They don’t capture bias at all. If there’s bias, the confidence interval or p-value can be meaningless.

What about models that epidemiologists don’t use? We have developed new methods as well (SCCS). we continue to do that, but it’s a hard problem.

Challenge for the students: we ran 5000 different analyses. Is there a good way of combining them to do better? weighted average? voting methods across different strategies?

Note the stuff is publicly available and might make a great Ph.D. thesis.

## Columbia Data Science course, week 9: Morningside Analytics, network analysis, data journalism

Our first speaker this week in Rachel Schutt‘s Columbia Data Science course was John Kelly from Morningside Analytics, who came to talk to us about network analysis.

John Kelly

Kelly has four diplomas from Columbia, starting with a BA in 1990 from Columbia College, followed by a Masters, MPhil and Ph.D. in Columbia’s school of Journalism. He explained that studying communications as a discipline can mean lots of things, but he was interested in network sociology and statistics in political science.

Kelly spent a couple of terms at Stanford learning survey design and game theory and other quanty stuff. He describes the Columbia program in communications as a pretty DIY set-up, where one could choose to focus on the role of communication in society, the impact of press, impact of information flow, or other things. Since he was interested in quantitative methods, he hunted them down, doing his master’s thesis work with Marc Smith from Microsoft. He worked on political discussions and how they evolve as networks (versus other kinds of discussions).

After college and before grad school, Kelly was an artist, using computers to do sound design. He spent 3 years as the Director of Digital Media here at Columbia School of the Arts.

Kelly taught himself perl and python when he spent a year in Viet Nam with his wife.

Kelly’s profile

Kelly spent quite a bit of time describing how he sees math, statistics, and computer science (including machine learning) as tools he needs to use and be good at in order to do what he really wants to do.

But for him the good stuff is all about domain expertise. He want to understand how people come together, and when they do, what is their impact on politics and public policy. His company Morningside Analytics has clients like think tanks and political organizations and want to know how social media affects and creates politics. In short, Kelly wants to understand society, and the math and stats allows him to do that.

Communication and presentations are how he makes money, so that’s important, and visualizations are integral to both domain expertise and communications, so he’s essentially a viz expert. As he points out, Morningside Analytics doesn’t get paid to just discover interesting stuff, but rather to help people use it.

Whereas a company such SocialFlow is venture funded, which means you can run a staff even if you don’t make money, Morningside is bootstrapped. It’s a different life, where we eat what we sow.

Case-attribute data vs. social network data

Kelly has a strong opinion about standard modeling through case-attribute data, which is what you normally see people feed to models with various “cases” (think people) who have various “attributes” (think age, or operating system, or search histories).

Maybe because it’s easy to store in databases or because it’s easy to collect this kind of data, there’s been a huge bias towards modeling with case-attribute data.

Kelly thinks it’s missing the point of the questions we are trying to answer nowadays. It started, he said, in the 1930′s with early market research, and it was soon being applied applied to marketing as well as politicals.

He named Paul Lazarsfeld and Elihu Katz as trailblazing sociologists who came here from Europe and developed the field of social network analysis. This is a theory based not only on individual people but also the relationships between them.

We could do something like this for the attributes of a data scientist, and we  might have an arrow point from math to stats if we think math “underlies” statistics in some way. Note the arrows don’t always mean the same thing, though, and when you specify a network model to test a theory it’s important you make the arrows well-defined.

To get an idea of why network analysis is superior to case-attribute data analysis, think about this. The federal government spends money to poll people in Afghanistan. The idea is to see what citizens want and think to determine what’s going to happen in the future. But, Kelly argues, what’ll happen there isn’t a function of what individuals think, it’s a question of who has the power and what they think.

Similarly, imagine going back in time and conducting a scientific poll of the citizenry of Europe in 1750 to determine the future politics. If you knew what you were doing you’d be looking at who’s marrying who among the royalty.

In some sense the current focus on case-attribute data is a problem of what’s “under the streetlamp” – people are used to doing it that way.

Kelly wants us to consider what he calls the micro/macro (i.e. individual versus systemic) divide: when it comes to buying stuff, or voting for a politician in a democracy, you have a formal mechanism for bridging the micro/macro divide, namely markets for buying stuff and elections for politicians. But most of the world doesn’t have those formal mechanisms, or indeed they have a fictive shadow of those things. For the most part we need to know enough about the actual social network to know who has the power and influence to bring about change.

Kelly claims that the world is a network much more than it’s a bunch of cases with attributes. For example, if you only understand how individuals behave, how do you tie things together?

History of social network analysis

Social network analysis basically comes from two places: graph theory, where Euler solved the Seven Bridges of Konigsberg problem, and sociometry, started by Jacob Moreno in the 1970′s, just as early computers got good at making large-scale computations on large data sets.

Social network analysis was germinated by Harrison White, emeritus at Columbia (emeritus), contemporaneously with Columbia sociologist Robert Merton. Their essential idea was that people’s actions have to be related to their attributes, but to really understand them you also need to look at the networks that enable them to do something.

Core entities for network models

Kelly gave us a bit of terminology from the world of social networks:

• actors (or nodes in graph theory speak): these can be people, or websites, or what have you
• relational ties (edges in graph theory speak): for example, an instance of liking someone or being friends
• dyads: pairs of actors
• triads: triplets of actors; there are for example, measures of triadic closure in networks
• subgroups: a subset of the whole set of actors, along with their relational ties
• group: the entirety of a “network”, easy in the case of Twitter but very hard in the case of e.g. “liberals”
• relation: for example, liking another person
• social network: all of the above

Types of Networks

There are different types of social networks.

For example, in one-node networks, the simplest case, you have a bunch of actors connected by ties. This is a construct you’d use to display a Facebook graph for example.

In two-node networks, also called bipartite graphs, the connections only exist between two formally separate classes of objects. So you might have people on the one hand and companies on the other, and you might connect a person to a company if she is on the board of that company. Or you could have people and the things they’re possibly interested in, and connect them if they really are.

Finally, there are ego networks, which is typically the part of the network surrounding a single person. So for example it could be just the subnetwork of my friends on Facebook, who may also know each other in certain cases. Kelly reports that people with higher socioeconomic status have more complicated ego networks. You can see someone’s level of social status by looking at their ego network.

What people do with these networks

The central question people ask when given a social network is, who’s important here?

This leads to various centrality measures. The key ones are:

1. degree – This counts how many people are connected to you.
2. closeness – If you are close to everyone, you have a high closeness score.
3. betweenness – People who connect people who are otherwise separate. If information goes through you, you have a high betweenness score.
4. eigenvector – A person who is popular with the popular kids has high eigenvector centrality. Google’s page rank is an example.

A caveat on the above centrality measures: the measurement people form an industry that try to sell themselves as the authority. But experience tells us that each has their weaknesses and strengths. The main thing is to know you’re looking at the right network.

For example, if you’re looking for a highly influential blogger in the muslim brotherhood, and you write down the top 100 bloggers in some large graph of bloggers, and start on the top of the list, and go down the list looking for a muslim brotherhood blogger, it won’t work: you’ll find someone who is both influential in the large network and who blogs for the muslim brotherhood, but they won’t be influential with the muslim brotherhood, but rather with transnational elites in the larger network. In other words, you have to keep in mind the local neighborhood of the graph.

Another problem with measures: experience dictates that, although something might work with blogs, when you work with Twitter you’ll need to get out new tools. Different data and different ways people game centrality measures make things totally different. For example, with Twitter, people create 5000 Twitter bots that all follow each other and some strategic other people to make them look influential by some measure (probably eigenvector centrality). But of course this isn’t accurate, it’s just someone gaming the measures.

Some network packages exist already and can compute the various centrality measures mentioned above:

Thought experiment

You’re part of an elite, well-funded think tank in DC. You can hire people and you have \$10million to spend. Your job is to empirically predict the future political evolution of Egypt. What kinds of political parties will there be? What is the country of Egypt gonna look like in 5, 10, or 20 years? You have access to exactly two of the following datasets for all Egyptians:

1. The Facebook network,
2. The Twitter network,
3. A complete record of who went to school with who,
4. The SMS/phone records,
5. The network data on members of all political organizations and private companies, and
6. Where everyone lives and who they talk to.

Note things change over time- people might migrate off of Facebook, or political discussions might need to go underground if blogging is too public. Facebook alone gives a lot of information but sometimes people will try to be stealth. Phone records might be better representation for that reason.

If you think the above is ambitious, recall Siemens from Germany sold Iran software to monitor their national mobile networks. In fact, Kelly says, governments are putting more energy into loading field with allies, and less with shutting down the field. Pakistan hires Americans to do their pro-Pakistan blogging and Russians help Syrians.

In order to answer this question, Kelly suggests we change the order of our thinking. A lot of the reasoning he heard from the class was based on the question, what can we learn from this or that data source? Instead, think about it the other way around: what would it mean to predict politics in a society? what kind of data do you need to know to do that? Figure out the questions first, and then look for the data to help me answer them.

Morningside Analytics

Kelly showed us a network  map of 14 of the world’s largest blogospheres. To understand the pictures, you imagine there’s a force, like a wind, which sends the nodes (blogs) out to the edge, but then there’s a counteracting force, namely the links between blogs, which attach them together.

Here’s an example of the arabic blogosphere:

The different colors represent countries and clusters of blogs. The size of each dot is centrality through degree, so the number of links to other blogs in the network. The physical structure of the blogosphere gives us insight.

If we analyze text using NLP, thinking of the blog posts as a pile of text or a river of text, then we see the micro or macro picture only – we lose the most important story. What’s missing there is social network analysis (SNA) which helps us map and analyze the patterns of interaction.

The 12 different international blogospheres, for example, look different. We infer that different societies have different interests which give rise to different patterns.

But why are they different? After all, they’re representations of some higher dimensional thing projected onto two dimensions. Couldn’t it be just that they’re drawn differently? Yes, but we do lots of text analysis that convinces us these pictures really are showing us something. We put an effort into interpreting the content qualitatively.

So for example, in the French blogosphere, we see a cluster that discusses gourmet cooking. In Germany we see various blobs discussing politics and lots of weird hobbies. In English we see two big blobs [mathbabe interjects: gay porn and straight porn?] They turn out to be conservative vs. liberal blogs.

In Russian, their blogging networks tend to force people to stay within the networks, which is why we see very well defined partitioned blobs.

The proximity clustering is done using the Fruchterman-Reingold algorithm, where being in the same neighborhood means your neighbors are connected to other neighbors, so really a collective phenomenon of influence.. Then we interpret the segments. Here’s an example of English language blogs:

Think about social media companies: they are each built around the fact that they either have the data or that they have a toolkit – a patented sentiment engine or something, a machine that goes ping.

But keep in mind that social media is heavily a product of organizations that pay to move the needle (i.e. game the machine that goes ping). To decipher that game you need to see how it works, you need to visualize.

So if you are wondering about elections, look at people’s blogs within “the moms” or “the sports fans”. This is more informative than looking at partisan blogs where you already know the answer.

Kelly walked us through an analysis, once he has binned the blogosphere into its segments, of various types of links to partisan videos like MLK’s “I have a dream” speech and a gotcha video from the Romney campaign. In the case of the MLK speech, you see that it gets posted in spurts around the election cycle events all over the blogosphere, but in the case of the Romney campaign video, you see a concerted effort by conservative bloggers to post the video in unison.

That is to say, if you were just looking at a histogram of links, a pure count, it might look as if it had gone viral, but if you look at it through the lens of the understood segmentation of the blogosphere, it’s clearly a planned operation to game the “virality” measures.

Kelly also works with the Berkman Center for Internet and Society at Harvard. He analyzed the Iranian blogosphere in 2008 and again in 2011 and he found much the same in terms of clustering – young anti-government democrats, poetry, conservative pro-regime clusters dominated in both years.

However, only 15% of the blogs are the same 2008 to 2011.

So, whereas people are often concerned about individuals (case-attribute model), the individual fish are less important than the schools of fish. By doing social network analysis, we are looking for the schools, because that way we learn about the salient interests of the society and how those interests are they stable over time.

The moral of this story is that we need to focus on meso-level patterns, not micro- or macro-level patterns.

John Bruner

Our second speaker of the night was John Bruner, an editor at O’Reilly who previously worked as the data editor at Forbes. He is broad in his skills: he does research and writing on anything that involved data. Among other things at Forbes, he worked on an internal database on millionaires on which he ran simple versions of social media dynamics.

Writing technical journalism

Bruner explained the term “data journalism” to the class. He started this by way of explaining his own data scientist profile.

First of all, it involved lots of data viz. A visualization is a fast way of describing the bottomline of a data set. And at a big place like the NYTimes, data viz is its own discipline and you’ll see people with expertise in parts of dataviz – one person will focus on graphics while someone else will be in charge of interactive dataviz.

CS skills are pretty important in data journalism too. There are tight deadlines, and the data journalist has to be good with their tools and with messy data (because even federal data is messy). One has to be able to handle arcane formats or whatever, and often this means parcing stuff in python or what have you. Bruner uses javascript and python and SQL and Mongo among other tools.

Bruno was a math major in college at University of Chicago, then he went into writing at Forbes, where he slowly merged back into quantitative stuff while there. He found himself using mathematics in his work in preparing good representations of the research he was uncovering about, for example, contributions of billionaires to politicians using circles and lines.

Statistics, Bruno says, informs the way you think about the world. It inspires you to write things: e.g., the “average” person is a woman with 250 followers but the median open twitter account has 0 followers. So the median and mean are impossibly different because the data is skewed. That’s an inspiration right there for a story.

Bruno admits to being a novice in machine learning.However, he claims domain expertise as quite important. With exception to people who can specialize in one subject, say at a governmental office or a huge daily, for smaller newspaper you need to be broad, and you need to acquire a baseline layer of expertise quickly.

Of course communications and presentations are absolutely huge for data journalists. Their fundamental skill is translation: taking complicated stories and deriving meaning that readers will understand. They also need to anticipate questions, turn them into quantitative experiments, and answer them persuasively.

A bit of history of data journalism

Data journalism has been around for a while, but until recently (computer-assisted reporting) was a domain of Excel power users. Still, if you know how to write an excel program, you’re an elite.

Things started to change recently: more data became available to us in the form of API’s, new tools and less expensive computing power, so we can analyze pretty large data sets on your laptop. Of course excellent viz tools make things more compelling, flash is used for interactive viz environments, and javascript is getting way better.

Programming skills are now widely enough held so that you can find people who are both good writers and good programmers. Many people are english majors and know enough about computers to make it work, for example, or CS majors who can write.

In big publications like the NYTimes, the practice of data journalism is divided into fields: graphics vs. interactives, research, database engineers, crawlers, software developers, domain expert writers. Some people are in charge of raising the right questions but hand off to others to do the analysis. Charles Duhigg at the NYTimes, for example, studied water quality in new york, and got a FOIA request to the State of New York, and knew enough to know what would be in that FOIA request and what questions to ask but someone else did the actual analysis.

At a smaller place, things are totally different. Whereas the NYTimes has 1000 people on its newsroom floor, the Economist has maybe 130, and Forbes has 70 or 80 people in their newsrooms. If you work for anything beside a national daily, you end up doing everything by yourself: you come up with question, you go get the data, you do the analysis, then you write it up.

Of course you also help and collaborate with your colleagues when you can.

Advice Bruno has for the students in initiating a data journalism project: don’t have a strong thesis before you’ve interviewed the experts. Go in with a loose idea of what you’re searching for and be willing to change your mind and pivot if the experts lead you in a new and interesting direction.