mathbabe

I recently posted about the new, free online course Model Thinking. I’ve watched more videos now and I am prepared to make more comments.

For the record, the lecturer, Scott Page, is by all accounts a great guy, and indeed he seems super nice on video. I’d love to have him over for dinner with my family someday (Professor Page, please come to my house for dinner when you’re in town).

In spite of liking him, though, pretty much every example he gives as pro-modeling is, for me, an anti-modeling example. Maybe I should make a complementary series of YouTube comment videos. It’s not totally true, of course- I just probably don’t notice the things we agree on. But I do notice the topics on which we disagree:

1. He talks a lot about how models make us clearer thinkers. But what he really seems to mean is that they make us stupider thinkers. His example is that, in order to decide who to vote for for president, we can model this decision as depending on two things: the likability of the person in question (presumably he assumes we want our president to be likable), and the extent to which that person is “as left” or “as right” as we are. I don’t know about you, but I actually care about specific issues and where people stand on them, and which issues I consider likely to come up for consideration in the next election cycle. Like, if I like someone for his “stick it to the banks” approach but he’s anti-abortion, then I think about whether abortion is likely to actually become illegal. And by the way, I don’t particularly care if my president is likable, I’d rather have him or her effective.
2. He bizarrely chooses “financial interconnectedness” as a way of seeing how cool models are, and he shows a graph where the nodes are the financial institutions (Goldman Sachs, JP Morgan, etc.) and the edges are labeled with an interconnectedness score, bigger meaning more interconnected. He shows that, according to this graph, back in 2008 it shows we knew to bail out AIG but that it was definitely okay to let Lehman fail. I’m wondering if he really meant that this was an example of how your model could totally fail because your “interconnectedness scoring” sucked, but he didn’t seem to be tongue in cheek.
3. He then talked about measuring the segregation of a neighborhood, either by race or by income, and he used New York and Chicago as examples. I won’t go into lots of details, but he gave a score to each block, like the census maps do with coloring, and he used those scores to develop a new score which was supposed to measure the segregation of each block. The problem I have with this segregation score is that it depends very heavily on the definition of the overall area you are considering. If you enlarge your definition of the New York City to include the suburbs, then the segregation score of New York City may (probably would) be completely different. This seems to be a really terrible characteristic of such a metric.
4. My second problem with his segregation score is that, at the end, he had overall segregation numbers for Philly and Detroit, and then showed the maps and mentioned that, looking at the maps, you wouldn’t really notice that one is more segregated than the other (Philly more than Detroit), but knowing the scores you do know that. Umm.. I’d like to rather say, if you are getting scores that are not fundamentally obvious from looking at these pictures, then maybe it’s because your score sucks. What does having a “good segregation score” mean if not that it captures something you can see through a picture?
5. One thing I liked was a demonstration of Schelling’s Segregation Model, which shows that, if you have a group of people who are not all that individually racist, you can still end up with a neighborhood which is very segregated.

I’m looking forward to watching more videos with my skeptical eye. After all, the guy is really a sweetheart, and I do really care about the idea of teaching people about modeling.

I really feel like I can’t keep up with all of the creepy models coming out and the news articles about them, so I think I’ll just start making a list. I would appreciate readers adding to my list in the comment section. I think I’ll move this to a separate page on my blog if it comes out nice.

1. I recently blogged about a model that predicts student success in for-profit institutions, which I claim is really mostly about student debt and default,
2. but here’s a model which actually goes ahead and predicts default directly, it’s a new payday-like loan model. Oh good, because the old payday models didn’t make enough money or something.
3. Of course there’s the teacher value-added model which I’ve blogged about multiple times, most recently here. And here’s a paper I’d like everyone to read before they listen to anyone argue one way or the other about the model (h/t Joshua Batson). The abstract is stunning: Recently, educational researchers and practitioners have turned to value-added models to evaluate teacher performance. Although value-added estimates depend on the assessment used to measure student achievement, the importance of outcome selection has received scant attention in the literature. Using data from a large, urban school district, I examine whether value-added estimates from three separate reading achievement tests provide similar answers about teacher performance. I find moderate-sized rank correlations, ranging from 0.15 to 0.58, between the estimates derived from different tests. Although the tests vary to some degree in content, scaling, and sample of students, these factors do not explain the differences in teacher effects. Instead, test timing and measurement error contribute substantially to the instability of value-added estimates across tests. Just in case that didn’t come through, they are saying that the results of the teacher value-added test scores are very very noisy.
4. That reminds me, credit scoring models are old but very very creepy, wouldn’t you agree? What’s in them that they want to conceal them?
5. Did you read about how Target predicts pregnancy? Extremely creepy.
6. I’m actually divided about whether it’s the creepiest though, because I think the sheer enormity of information that Facebook collects about us is the most depressing thing of all.

Before I became a modeler, I wasn’t personally offended by the idea that people could use my information. I thought, I’ve got nothing to hide, and in fact maybe it will make my life easier and more efficient for the machine to know me and my habits.

But here’s how I think now that I’m a modeler and I see how this stuff gets made and I see how it gets applied. That we are each giving up our data, and it’s so easy to do we don’t think about it, and it’s being used to funnel people into success or failure in a feedback loop. And the modelers, the people responsible for creating these things and implementing them, are always already the successes, they are educated and are given good terms on their credit cards and mortgages because they have a nifty high tech job. So the makers get to think of how much easier and more convenient their lives are now that the models see how dependable they are as consumers.

But when there are funnels, there’s always someone who gets funneled down.

Think about how it works with insurance. The idea of insurance is to pool people so that when one person gets sick, the medical costs for that person are paid from the common fund. Everyone pays a bit so it doesn’t break the bank.

But if we have really good information, we begin to see how likely people are to get sick. So we can stratify the pool. Since I almost never get sick, and when I do it’s just strep throat, I get put into a very nice pool with other people who never get sick, and we pay very very little and it works out great for us. But other people have worse luck of the DNA draw and they get put into the “pretty sick” pool and their premium gets bigger as their pool gets sicker until they are really sick and the premium is actually unaffordable. We are left with a system where the people who need insurance the most can’t be part of the system anymore. Too much information ruins the whole idea of insurance and pooled risk.

I think modern modeling is analogous. When people offer deals, they can first check to see if the people they are offering deals are guaranteed to pay back everything. In other words, the businesses (understandably) want to make very certain they are going to profit from each and every customer, and they are getting more and more able to do this. That’s great for customers with perfect credit scores, and it makes it easier for people with perfect credit scores to keep their perfect credit scores, because they are getting the best deals.

But for people with bad credit scores, they get the rottenest deals, which makes a larger and larger percentage of their takehome pay (if they even get a job considering their credit scores) go towards fees and high interest rates. This of course creates an environment in which it’s difficult to improve their credit score- so they default and their credit score gets worse instead of better.

So there you have it, a negative feedback loop and a death spiral of modeling.

I recently read this New York Times article about a company that figures out how to get the best deal when you rent a car. The company is called AutoSlash and the idea is you book with them and they keep looking for good deals, coupons, or free offers every day until you actually need the car.

Wait a minute, a data science model that actually directly improves the lives of its customers? Why can’t we have more of these? Obviously the car companies absolutely hate this idea. But what are they going to do, stop offering online shopping?

Why don’t we see this in every category of shopping? It seems to me that you could do something like this and start a meta-marketplace, where you buy something and then, depending on how long you’re willing to wait until delivery, the model looks for a better online deal, in exchange for a small commission. Then you’d have to make sure that on average the commission is paying for itself with better deals, but my guess is it would work if you allowed it a few days to search per purchase. Or if you really are a doubter, fix a minimum wait time and let the company take some (larger) percentage of the difference between the initial price and the eventual best price.

Another way of saying this, is that when you go online to buy something, depending on the scale (say it’s on the expensive side) you probably shop around for a few days or weeks. Why do that in person? Just have a computer do it for you and tell you at the end what deal it gave you. Don’t get bombarded by ads, let the computer get bombarded by ads for you.

I was recently at a Meetup and got into a discussion with Joey Markowitz about the difference between supervised, unsupervised, and partially (semi-) supervised learning.

For those who haven’t heard of this stuff, a bit of explanation. These are general categories of models. In every model there’s input data, and in some models there’s also a known quantity you are trying to predict, starting from the input data.

Not surprisingly, supervised learning is what finance quants do, because they always know what they’re going to predict: the money. Unsupervised means you don’t really know what you are looking for in advance. A good example of this is “clustering” algorithms, where you input the data and the number of clusters and the algorithm finds the “best” way of clustering the data into that many clusters (with respect to some norm in N-space where N is the number of attributes of the input data). As a toy example, you could have all your friends write down how much they like various kinds of foods (tofu, broccoli, garlic, ice cream, buttered toast) and after clustering you might find a bunch of people live in the “we love tofu, broccoli, and garlic” cluster and the others live over in the “we love ice cream and buttered toast” cluster.

I hadn’t heard of the phrase “partially supervised learning,” but it turns out it just means you train your model both on labeled and unlabeled data. Usually there’s a domain expert who doesn’t have time to classify all of the data, but the algorithm is augmented by their partial information. So, again a toy example, if the algorithm is classifying photographs, it may help for a human to go through some of them and classify them “porn” vs. “not porn” (because I know it when I see it).

Joey had some interesting thoughts about what’s really going on with supervised vs. unsupervised; he claims that “unsupervised” should really be called “indirectly supervised”. He followed up with this email:

I currently think about unsupervised learning as indirectly supervised learning.  The primary reason is because once you implement an unsupervised learning algorithm it eventually becomes part of a large package, and that larger package is evaluated.  Indirectly you can back out from the package evaluation the effectiveness of different implementations/seeds of the unsupervised learning algorithm.

So simply put, the unsupervised learning algorithm is only unsupervised in isolation, and indirectly supervised once part of a larger picture.  If you distill this further the evaluation metric for unsupervised algorithms are project specific and developed through error analysis whereas for supervised algorithms the metric is specific to the algorithm, irrespective to the project.

supervised learning:        input data -> learning algorithm -> problem non-specific cost metric -> output

unsupervised learning:    input data -> learning algorithm -> problem specific cost metric -> output

The main question is… once you formulate evaluation metric for an unsupervised algorithm specific to your project… can it still be called unsupervised?

This is a good question. One stupid example of this is that, if in the tofu-broccoli-ice cream example above, we had forced three clusters instead of the more natural two clusters, then after we look at the result we may say, shit this is really a two-cluster problem. That moment when we switch the number of clusters to two is, of course, supervising the so-called unsupervised process.

I think though that Joey’s remark runs deeper than that, and is perhaps an example of how we trick ourselves into thinking we’ve successfully algorithmized a process when in fact we have made an awful lot of choices.

In this recent article in the Wall Street Journal, we are presented with two sides of a debate on whether there should be a unique medical identifier given to each patient in the U.S. healthcare system.

Both sides agree that this would help record keeping problems so much (compared to the shambles that exist today) that it would vastly improve scientists’ ability to understand and predict disease. But the personal privacy issues are sufficiently worrying for some people to conclude that the benefits do not outweigh the risks.

Once it’s really easy to track people and their medical data through the system, the data can and will be exploited for commercial purposes or worse (imagine your potential employer looking up your entire medical record in addition to your prison record and credit score).

I agree with both sides, if that’s possible, although they both have flaws: the pro-identifier trivializes the problems of computer security, and the anti-identifier trivializes the field of data anonymization. It’s just incredibly frustrating that we haven’t been able to come to some reasonable solution to this that protects individual identities while letting the record keeping become digitized and reasonable.

Done well, a functional system would have the potential to save people’s lives in the millions while not exposing vulnerable people to more discrimination and suffering. Done poorly and without serious thought, we could easily have the worst of all worlds, where corporations have all the data they can pay for and where only rich people have the ability or influence to opt out of the system.

Let’s get it together, people! We need scientists and lawyers and privacy experts and ethicists and data nerds to get together and find some intelligently thought-out middle ground.

Prediction: in the next 10 years we will see the majority of major universities start masters degree programs, or Ph.D. programs, in data science, data analytics, business analytics, or the like. They will exist somewhere in the intersection of the fields of statistics, operations research, and computer science, and business. They will teach students how to use machine learning algorithms and various statistical methods, and how to design expert systems. Then they will send these newly minted data scientists out to work at McKinsey, Google, Yahoo, and possibly Data Without Borders.

The questions yet unanswered:

• Relevance: will they also teach the underlying theory well enough so that the students will know when the techniques are applicable?
• Skepticism: will they in general teach enough about robustness in order for the emerging data scientists to be sufficiently skeptical of the resulting models?
• Ethics: will they incorporate understanding the impact of the models so that students will think to understand the ethical implications of modeling? Will they have a well-developed notion of the Modeler’s Hippocratic Oath by then?
• Open modeling: will they focus narrowly on making businesses more efficient or will they focus on developing platforms which are open to the public and allow people more views into the models, especially when the models in question affect that public?

Open questions. And important ones.

Here’s one that’s already been started at the University of North Carolina, Charlotte.

If you saw this story going around about how statisticians can predict the activity of serial killers, be sure to read this post by Cosma Shalizi where he brutally tears down the underlying methodology. My favorite part:

Since Simkin and Roychowdhury’s model produces a power law, and these data, whatever else one might say about them, are not power-law distributed, I will refrain from discussing all the ways in which it is a bad model. I will re-iterate that it is an idiotic paper — which is different from saying that Simkin and Roychowdhury are idiots; they are not and have done interesting work on, e.g., estimating how often references are copied from bibliographies without being read by tracking citation errors⁴. But the idiocy in this paper goes beyond statistical incompetence. The model used here was originally proposed for the time intervals between epileptic fits. The authors realize that

[i]t may seem unreasonable to use the same model to describe an epileptic and a serial killer. However, Lombroso [5] long ago pointed out a link between epilepsy and criminality.

That would be the 19th-century pseudo-scientist³ Cesare Lombroso, who also thought he could identify criminals from the shape of their skulls; for “pointed out”, read “made up”. Like I said: idiocy.

Next, if you’re anything like me, you’ve had way too many experiences giving birth without pain control, even after begging continuously and profusely for some, because of some poorly derived statistical criterion that should never have been applied to anyone. This article debunks that among others related to babies and childbirth.

In particular, it suggests what I always suspected, namely that people misunderstand the effect of using epidurals because they don’t control for the fact that in the case of a long difficult birth you are more likely to get everything, which brings down the average outcome among people with epidurals but doesn’t at all prove causation.

Pregnant ladies, I suggest you print out this article and bring it with you to your OB appointments.

A few weeks ago I was a “data wrangler” at the first Data Without Borders datadive weekend. My group of volunteer data scientists was exploring the NYPD “Stop, Question and Frisk” data from the previous few years. I blogged about it here and here.

One thing we were interested in exploring was the extent to which this policy, whereby people can be stopped, questioned, and frisked for merely looking suspicious (to the cops) is racist. This is what I said in my second post:

We read Gelman, Fagan and Kiss’s article about using the Stop and Frisk data to understand racial profiling, with the idea that we could test it out on more data or modify their methodology to slightly change the goal. However, they used crime statistics data that we don’t have and can’t find and which are essential to a good study.

As an example of how crucial crime data like this is, if you hear the statement, “10% of the people living in this community are black but 50% of the people stopped and frisked are black,” it sounds pretty damning, but if you add “50% of crimes are committed by blacks” then it sound less so. We need that data for the purpose of analysis.

Why is crime statistics data so hard to find? If you go to NYPD’s site and search for crime statistics, you get really very little information, which is not broken down by area (never mind x and y coordinates) or ethnicity. That stuff should be publicly available. In any case it’s interesting that the Stop and Frisk data is but the crime stats data isn’t.

I still think it is outrageous that we don’t have open source crime statistics in New York, where Bloomberg claims to be such a friend to data and to openness.

And I also still think that, in order to prove racism in the strict sense of the above discussion, we need that data.

However, my overall opinion has changed about whether we have enough data already to say if this policy is broadly racist. It is. My mind changed reading this article from the New York Times a couple of weeks ago. It was written by a young black man from New York, describing his experiences first-hand being stopped, questioned, and frisked. The entire article is excellently written and you should take a look; here’s an excerpt:

For young people in my neighborhood, getting stopped and frisked is a rite of passage. We expect the police to jump us at any moment. We know the rules: don’t run and don’t try to explain, because speaking up for yourself might get you arrested or worse. And we all feel the same way — degraded, harassed, violated and criminalized because we’re black or Latino. Have I been stopped more than the average young black person? I don’t know, but I look like a zillion other people on the street. And we’re all just trying to live our lives.

The argument for this policy is that it improves crime statistics. For some people, especially if they aren’t young and aren’t constant targets of the policy, it’s probably a price worth paying to live in a less crime-ridden area.

And we all want there to be less crime, of course, but what we really want is something even more fundamental, which is a high quality of life. Part of that is not being victimized by crooks, but another part of that is not being (singled out and) victimized by authority either.

I think a good thought experiment is to consider how they could make the policy colorblind. One obvious way is to have cops in every neighborhood performing stop, question and frisk to random people. The argument against this is, of course, that we don’t have enough cops or enough money to do something like that.

Instead, to be more realistic about resources, we could have groups of cops randomly be assigned to neighborhoods on a given day for such stops. If you think the policy is such a good crime deterrent, than you can even weight the probability of a given neighborhood by the crime rate in that neighborhood. (As an aside, I would love to see whether there’s statistically significant reason to believe that this policy does, in fact, deter crime. So often mayors and policies take credit for lowered crime rates in a given city when in fact crime rates are going down all over the country in a kind of seasonality way.) So in this model the cops are more likely to land in a high-crime area, but eventually by the laws of statistics they will visit every neighborhood.

My guess is that, the very first time the Upper East Side is chosen randomly, and a white hedge fund manager is stopped, questioned, and frisked by a cop, who takes away his key and enters his apartment, terrorizing his family while he’s handcuffed in the back of a cop car, is the very last day this policy is in place.

As a data scientist at an internet start-up, I am something of a quantitative handyman. I go where there is need for quantitative thinking. Since the business model of my company is super quantitative, this means I have lots of work. I have recently categorized the kind of things I do into 4 bins:

1. I visualize data for business people to digest. This is a kind of fancy data science-y way of saying I design reports. It’s actually a hugely critical part of the business, since our clients are less quantitative than we are and need to feel like they understand the situation, so clear, honest, and easily digestible visuals is a priority.
2. I forecast behavior using models. This means I forecast what users on a website will do, based on their attributes and historical precedent for what people who shared their attributes did in the past, and I also do things like stress test the business itself, in order to answer questions like, what would happen to our revenue stream if one of our advertisers jumped out of the auction?
3. I measure. This is where the old-school statistics comes in, in deciding whether things are statistically significant and what is our confidence interval. It’s related to reporting as well, but it’s a separate task.
4. I help decide whether business ideas are quantitatively reasonable. Will there be enough data to answer this question? How long will we need to collect data to have a statistically significant answer to that? This is kind of like being a McKinsey consultant on data steroids.

So why is it so hard to find a good data scientist?

Here’s why. Most data scientists don’t really think that 3 and 4 above are their job. It is far less sexy to try to honestly find the confidence interval of a prediction than it is to model behavior. Data scientists are considered magical when they forecast behavior that was hitherto unknown, and they are considered total downers when they tell their CEO, hey there’s just not enough data to start that business you want to start, or hey this data is actually really fat-tailed and our confidence intervals suck.

In other words, it’s something like what the head of risk management had to face at a big bank taking risks in 2007. There’s a responsibility to warn people that too much confidence in the models is bad, but then there’s the political reality of the situation, where you just want to be liked and you don’t actually have the power to stop the relevant decisions anyway. And there’s the added issue in a start-up that they are your models, and you want them to be liked (and to be invincible).

It’s far easier to focus on visualizing and modeling, or to stay even sexier and more mystical, just modeling itself, and let the business make decisions that could ultimately not work out, or act on data that’s pure noise.

How do you select for a good data scientist? Look for one that speaks clearly, directly, and emphasizes skepticism. Look for one that is ready to vent about how people trust models too much, and also someone who’s pushy enough to speak up at a meeting and be that annoying person who holds people back from drinking too much kool-aid.