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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 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 the treatment (so, Frank using the word “beautiful” in the email). We usually assume this to have a binary (0/1) outcome.

Denote by 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 ).
3. Translate question into a formal quantity (denote this by ).
4. Estimate quantity (denote this by ).

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

where

• denotes the baseline variables (attributes of the agent) as above,
• denotes the binary treatment as above,
• denotes the binary outcome if treated, and
• 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:

Note that, since and are binary, the expected value 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:

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 exogenous variables, i.e. stuff we’re ignoring. Assume there are functions and so that:

• i.e. the attributes are just functions of some exogenous variables,
• i.e. the treatment depends in a nice way on some exogenous variables as well the attributes we know about living in , and
• i.e. the outcome is just a function of the treatment, the attributes, and some exogenous variables.

Note the various ‘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 on outcome ?

Let’s look at this from the point of view of the joint distribution 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:

i.e. the probability knowing someone either got treated or not. To answer our question, we manipulate the value of 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 which by the above can be rewritten

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 and , which generate estimates of the probability of the treatment knowing the attributes (that’s machine ) and the probability of the outcome knowing the treatment and the attributes (machine ).

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 machine, i.e. the machine that estimates the treatment probability based on attributes. The problem is that people get the machine wrong all the time, which makes this method fail.

In words, when 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 and take the difference.

MLE

This method is based on the 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, and 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 and those not treated set collect attributes
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:

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:

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

Then the unit level causal effect is , but we only see one of and

Example: is 1 if I smoked, 0 if I didn’t (I am the unit). is 1 or 0 if I got cancer and I smoked, and is 1 or 0 depending on whether I got cancer while not smoking. The overall causal effect on me is the difference 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.

This week in Rachel Schutt’s Columbia Data Science course we had two excellent guest speakers.

The first speaker of the night was Mark Hansen, who recently came from UCLA via the New York Times to Columbia with a joint appointment in journalism and statistics. He is a renowned data visualization expert and also an energetic and generous speaker. We were lucky to have him on a night where he’d been drinking an XXL latte from Starbucks to highlight his natural effervescence.

Mark started by telling us a bit about Gabriel Tarde (1843-1904).

Tarde was a sociologist who believed that the social sciences had the capacity to produce vastly more data than the physical sciences. His reasoning was as follows.

The physical sciences observe from a distance: they typically model or incorporate models which talk about an aggregate in some way – for example, biology talks about the aggregate of our cells. What Tarde pointed out was that this is a deficiency, basically a lack of information. We should instead be tracking every atom.

This is where Tarde points out that in the social realm we can do this, where cells are replaced by people. We can collect a huge amount of information about those individuals.

But wait, are we not missing the forest for the trees when we do this? Bruno Latour weighs in on his take of Tarde as follows:

“But the ‘whole’ is now nothing more than a provisional visualization which can be modified and reversed at will, by moving back to the individual components, and then looking for yet other tools to regroup the same elements into alternative assemblages.”

In 1903, Tarde even foresees the emergence of Facebook, although he refers to a “daily press”:

“At some point, every social event is going to be reported or observed.”

Mark then laid down the theme of his lecture using a 2009 quote of Bruno Latour:

“Change the instruments and you will change the entire social theory that goes with them.”

Kind of like that famous physics cat, I guess, Mark (and Tarde) want us to newly consider

1. the way the structure of society changes as we observe it, and
2. ways of thinking about the relationship of the individual to the aggregate.

Mark’s Thought Experiment:

As data become more personal, as we collect more data about “individuals”, what new methods or tools do we need to express the fundamental relationship between ourselves and our communities, our communities and our country, our country and the world? Could we ever be satisfied with poll results or presidential approval ratings when we can see the complete trajectory of public opinions, individuated and interacting?

What is data science?

Mark threw up this quote from our own John Tukey:

“The best thing about being a statistician is that you get to play in everyone’s backyard”

But let’s think about that again – is it so great? Is it even reasonable? In some sense, to think of us as playing in other people’s yards, with their toys, is to draw a line between “traditional data fields” and “everything else”.

It’s maybe even implying that all our magic comes from the traditional data fields (math, stats, CS), and we’re some kind of super humans because we’re uber-nerds. That’s a convenient way to look at it from the perspective of our egos, of course, but it’s perhaps too narrow and arrogant.

And it begs the question, what is “traditional” and what is “everything else” anyway?

Mark claims that everything else should include:

• social science,
• physical science,
• geography,
• architecture,
• education,
• information science,
• architecture,
• digital humanities,
• journalism,
• design,
• media art

There’s more to our practice than being technologists, and we need to realize that technology itself emerges out of the natural needs of a discipline. For example, GIS emerges from geographers and text data mining emerges from digital humanities.

In other words, it’s not math people ruling the world, it’s domain practices being informed by techniques growing organically from those fields. When data hits their practice, each practice is learning differently; their concerns are unique to that practice.

Responsible data science integrates those lessons, and it’s not a purely mathematical integration. It could be a way of describing events, for example. Specifically, it’s not necessarily a quantifiable thing.

Bottom-line: it’s possible that the language of data science has something to do with social science just as it has something to do with math.

Processing

Mark then told us a bit about his profile (“expansionist”) and about the language processing, in answer to a question about what is different when a designer takes up data or starts to code.

He explained it by way of another thought experiment: what is the use case for a language for artists? Students came up with a bunch of ideas:

• being able to specify shapes,
• faithful rendering of what visual thing you had in mind,
• being able to sketch,
• 3-d,
• animation,
• interactivity,
• Mark added publishing – artists must be able to share and publish their end results.

It’s java based, with a simple “publish” button, etc. The language is adapted to the practice of artists. He mentioned that teaching designers to code meant, for him, stepping back and talking about iteration, if statements, etc., of in other words stuff that seemed obvious to him but is not obvious to someone who is an artist. He needed to unpack his assumptions, which is what’s fun about teaching to the uninitiated.

He next moved on to close versus distant reading of texts. He mentioned Franco Moretti from Stanford. This is for Franco:

Franco thinks about “distant reading”, which means trying to get a sense of what someone’s talking about without reading line by line. This leads to PCA-esque thinking, a kind of dimension reduction of novels.

In other words, another cool example of how data science should integrate the way the experts in various fields figure it out. We don’t just go into their backyards and play, maybe instead we go in and watch themplay and formalize and inform their process with our bells and whistles. In this way they can teach us new games, games that actually expand our fundamental conceptions of data and the approaches we need to analyze them.

Mark’s favorite viz projects

1) Nuage Vert, Helen Evans & Heiko Hansen: a projection onto a power plant’s steam cloud. The size of the green projection corresponds to the amount of energy the city is using. Helsinki and Paris.

2) One Tree, Natalie Jeremijenko: The artist cloned trees and planted the genetically identical seeds in several areas. Displays among other things the environmental conditions in each area where they are planted.

3) Dusty Relief, New Territories: here the building collects pollution around it, displayed as dust.

4) Project Reveal, New York Times R&D lab: this is a kind of magic mirror which wirelessly connects using facial recognition technology and gives you information about yourself. As you stand at the mirror in the morning you get that “come-to-jesus moment” according to Mark.

5) Million Dollar Blocks, Spatial Information Design Lab (SIDL): So there are crime stats for google maps, which are typically painful to look at. The SIDL is headed by Laura Kurgan, and in this piece she flipped the statistics. She went into the prison population data, and for every incarcerated person, she looked at their home address, measuring per home how much money the state was spending to keep the people who lived there in prison. She discovered that some blocks were spending $1,000,000 to keep people in prison.

Moral of the above: just because you can put something on the map, doesn’t mean you should. Doesn’t mean there’s a new story. Sometimes you need to dig deeper and flip it over to get a new story.

New York Times lobby: Moveable Type

Mark walked us through a project he did with Ben Rubin for the NYTimes on commission (and he later went to the NYTimes on sabbatical). It’s in the lobby of their midtown headquarters at 8th and 42nd.

It consists of 560 text displays, two walls with 280 on each, and the idea is they cycle through various “scenes” which each have a theme and an underlying data science model.

For example, in one there are waves upon waves of digital ticker-tape like scenes which leave behind clusters of text, and where each cluster represents a different story from the paper. The text for a given story highlights phrases which make a given story different from others in some information-theory sense.

In another scene the numbers coming out of stories are highlighted, so you might see on a given box “18 gorillas”. In a third scene, crossword puzzles play themselves with sounds of pencil and paper.

The display boxes themselves are retro, with embedded linux processors running python, and a sound card on each box, which makes clicky sounds or wavy sounds or typing sounds depending on what scene is playing.

The data taken in is text from NY Times articles, blogs, and search engine activity. Every sentence is parsed using Stanford NLP techniques, which diagrams sentences.

Altogether there are about 15 “scenes” so far, and it’s code so one can keep adding to it. Here’s an interview with them about the exhibit:

Project Cascade: Lives on a Screen

Mark next told us about Cascade, which was joint work with Jer Thorp data artist-in-residence at the New York Times. Cascade came about from thinking about how people share New York Times links on Twitter. It was in partnerships with bitly.

The idea was to collect enough data so that we could see someone browse, encode the link in bitly, tweet that encoded link, see other people click on that tweet and see bitly decode the link, and then see those new people browse the New York Times. It’s a visualization of that entire process, much as Tarde suggested we should do.

There were of course data decisions to be made: a loose matching of tweets and clicks through time, for example. If 17 different tweets have the same url they don’t know which one you clicked on, so they guess (the guess actually seemed to involve probabilistic matching on time stamps so it’s an educated guess). They used the Twitter map of who follows who. If someone you follow tweets about something before you do then it counts as a retweet. It covers any nytimes.com link.

Here’s a NYTimes R&D video about Project Cascade:

Note: this was done 2 years ago, and Twitter has gotten a lot bigger since then.

Cronkite Plaza

Next Mark told us about something he was working on which just opened 1.5 months ago with Jer and Ben. It’s also news related, but this is projecting on the outside of a building rather than in the lobby; specifically, the communications building at UT Austin, in Cronkite Plaza.

The majority of the projected text is sourced from Cronkite’s broadcasts, but also have local closed-captioned news sources. One scene of this project has extracted the questions asked during local news – things like “how did she react?” or “What type of dog would you get?”. The project uses 6 projectors.

Goals of these exhibits

They are meant to be graceful and artistic, but should also teach something. At the same time we don’t want to be overly didactic. The aim is to live in between art and information. It’s a funny place: increasingly we see a flattening effect when tools are digitized and made available, so that statisticians can code like a designer (we can make things that look like design) and similarly designers can make something that looks like data.

What data can we get? Be a good investigator: a small polite voice which asks for data usually gets it.

eBay transactions and books

Again working jointly with Jer Thorp, Mark investigated a day’s worth of eBay’s transactions that went through Paypal and, for whatever reason, two years of book sales. How do you visualize this? Take a look at the yummy underlying data:

Here’s how they did it (it’s ingenious). They started with the text of Death of a Salesman by Arthur Miller. They used a mechanical turk mechanism to locate objects in the text that you can buy on eBay.

When an object is found it moves it to a special bin, so “chair” or “flute” or “table.” When it has a few collected buy-able objects, it then takes the objects and sees where they are all for sale on the day’s worth of transactions, and looks at details on outliers and such. After examining the sales, the code will find a zipcode in some quiet place like Montana.

Then it flips over to the book sales data, looks at all the books bought or sold in that zip code, picks a book (which is also on Project Gutenberg), and begins to read that book and collect “buyable” objects from that. And it keeps going. Here’s a video:

Public Theater Shakespeare Machine

The last thing Mark showed us is is joint work with Rubin and Thorp, installed in the lobby of the Public Theater. The piece itself is an oval structure with 37 bladed LED displays, set above the bar.

There’s one blade for each of Shakespeare’s plays. Longer plays are in the long end of the oval, Hamlet you see when you come in.

The data input is the text of each play. Each scene does something different – for example, it might collect noun phrases that have something to do with body from each play, so the “Hamlet” blade will only show a body phrase from Hamlet. In another scene, various kinds of combinations or linguistic constructs are mined:

• “high and might” “good and gracious” etc.
• “devilish-holy” “heart-sore” “ill-favored” “sea-tossed” “light-winged” “crest-fallen” “hard-favoured” etc.

Note here that the digital humanities, through the MONK Project, offered intense xml descriptions of the plays. Every single word is given hooha and there’s something on the order of 150 different parts of speech.

As Mark said, it’s Shakespeare so it stays awesome no matter what you do, but here we see we’re successively considering words as symbols, or as thematic, or as parts of speech. It’s all data.

Ian Wong from Square

Next Ian Wong, an “Inference Scientist” at Square who dropped out of an Electrical Engineering Ph.D. program at Stanford talked to us about Data Science in Risk.

He conveniently started with his takeaways:

1. Machine learning is not equivalent to R scripts. ML is founded in math, expressed in code, and assembled into software. You need to be an engineer and learn to write readable, reusable code: your code will be reread more times by other people than by you, so learn to write it so that others can read it.
2. Data visualization is not equivalent to producing a nice plot. Rather, think about visualizations as pervasive and part of the environment of a good company.
3. Together, they augment human intelligence. We have limited cognitive abilities as human beings, but if we can learn from data, we create an exoskeleton, an augmented understanding of our world through data.

Square

Square was founded in 2009. There were 40 employees in 2010, and there are 400 now. The mission of the company is to make commerce easy. Right now transactions are needlessly complicated. It takes too much to understand and to do, even to know where to start for a vendor. For that matter, it’s too complicated for buyers as well. The question we set out to ask is, how do we make transactions simple and easy?

We send out a white piece of plastic, which we refer to as the iconic square. It’s something you can plug into your phone or iPad. It’s simple and familiar, and it makes it easy to use and to sell.

It’s even possible to buy things hands-free using the square. A buyer can open a tab on their phone so that they can pay by saying their name.. Then the merchant taps your name on their screen. This makes sense if you are a frequent visitor to a certain store like a coffee shop.

Our goal is to make it easy for sellers to sign up for Square and accept payments. Of course, it’s also possible that somebody may sign up and try to abuse the service. We are therefore very careful at Square to avoid losing money on sellers with fraudulent intentions or bad business models.

The Risk Challenge

At Square we need to balance the following goals:

1. to provide a frictionless and delightful experience for buyers and sellers,
2. to fuel rapid growth, and in particular to avoid inhibiting growth through asking for too much information of new sellers, which adds needless barriers to joining, and
3. to maintain low financial loss.

Today we’ll just focus on the third goal through detection of suspicious activity. We do this by investing in machine learning and viz. We’ll first discuss the machine learning aspects.

Part 1: Detecting suspicious activity using machine learning

First of all, what’s suspicious? Examples from the class included:

1. lots of micro transactions occurring,
2. signs of money laundering,
3. high frequency or inconsistent frequency of transactions.

Example: Say Rachel has a food truck, but then for whatever reason starts to have $1000 transactions (mathbabe can’t help but insert that Rachel might be a food douche which would explain everything).

On the one hand, if we let money go through, Square is liable in the case it was unauthorized. Technically the fraudster, so in this case Rachel would be liable, but our experience is that usually fraudsters are insolvent, so it ends up on Square.

On the other hand, the customer service is bad if we stop payment on what turn out to be real payments. After all, what if she’s innocent and we deny the charges? She will probably hate us, may even sully our reputation, and in any case our trust is lost with her after that.

This example crystallizes the important challenges we face: false positives erode customer trust, false negatives make us lose money.

And since Square processes millions of dollars worth of sales per day, we need to do this systematically and automatically. We need to assess the risk level of every event and entity in our system.

So what do we do?

First of all, we take a look at our data. We’ve got three types:

1. payment data, where the fields are transaction_id, seller_id, buyer_id, amount, success (0 or 1), timestamp,
2. seller data, where the fields are seller_id, sign_up_date, business_name, business_type, business_location,
3. settlement data, where the fields are settlement_id, state, timestamp.

Important fact: we settle to our customers the next day so we don’t have to make our decision within microseconds. We have a few hours. We’d like to do it quickly of course, but in certain cases we have time for a phone call to check on things.

So here’s the process: given a bunch (as in hundreds or thousands) of payment events, we throw each through the risk engine, and then send some iffy looking ones on to a “manual review”. An ops team will then review the cases on an individual basis. Specifically, anything that looks rejectable gets sent to ops, which make phone calls to double check unless it’s super outrageously obviously fraud.

Also, to be clear, there are actually two kinds of fraud to worry about, seller-side fraud and buyer-side fraud. For the purpose of this discussion, we’ll focus on the former.

So now it’s a question of how we set up the risk engine. Note that we can think of the risk engine as putting things in bins, and those bins each have labels. So we can call this a labeling problem.

But that kind of makes it sound like unsupervised learning, like a clustering problem, and although it shares some properties with that, it’s certainly not that simple – we don’t reject a payment and then merely stand pat with that label, because as we discussed we send it on to an ops team to assess it independently. So in actuality we have a pretty complicated set of labels, including for example:

• initially rejected but ok,
• initially rejected and bad,
• initially accepted but on further consideration might have been bad,
• initially accepted and things seem ok,
• initially accepted and later found to be bad, …

So in other words we have ourselves a semi-supervised learning problem, straddling the worlds of supervised and unsupervised learning. We first check our old labels, and modify them, and then use them to help cluster new events using salient properties and attributes common to historical events whose labels we trust. We are constantly modifying our labels even in retrospect for this reason.

We estimate performance  using precision and recall. Note there are very few positive examples so accuracy is not a good metric of success, since the “everything looks good” model is dumb but has good accuracy.

Labels are what Ian considered to be the “neglected half of the data” (recall T = {(x_i, y_i)}). In undergrad statistics education and in data mining competitions, the availability of labels is often taken for granted. In reality, labels are tough to define and capture. Labels are really important. It’s not just objective function, it is the objective.

As is probably familiar to people, we have a problem with sparsity of features. This is exacerbated by class imbalance (i.e., there are few positive samples). We also don’t know the same information for all of our sellers, especially when we have new sellers. But if we are too conservative we start off on the wrong foot with new customers.

Also, we might have a data point, say zipcode, for every seller, but we don’t have enough information in knowing the zipcode alone because so few sellers share zipcodes. In this case we want to do some clever binning of the zipcodes, which is something like sub model of our model.

Finally, and this is typical for predictive algorithms, we need to tweak our algorithm to optimize it- we need to consider whether features interact linearly or non-linearly, and to account for class imbalance.. We also have to be aware of adversarial behavior. An example of adversarial behavior in e-commerce is new buyer fraud, where a given person sets up 10 new accounts with slightly different spellings of their name and address.

Since models degrade over time, as people learn to game them, we need to continually retrain models. The keys to building performance models are as follows:

• it’s not a black box. You can’t build a good model by assuming that the algorithm will take care of everything. For instance, I need to know why I am misclassifying certain people, so I’ll need to roll up my sleeves and dig into my model.
• We need to perform rapid iterations of testing, with experiments like you’d do in a science lab. If you’re not sure whether to try A or B, then try both.
• When you hear someone say, “So which models or packages do you use?” then you’ve got someone who doesn’t get it. Models and/or packages are not magic potion.

Mathbabe cannot resist paraphrasing Ian here as saying “It’s not about the package. it’s about what you do with it.” But what Ian really thinks it’s about, at least for code, is:

• readability
• reusability
• correctness
• structure
• hygiene

So, if you’re coding a random forest algorithm and you’ve hardcoded the number of trees: you’re an idiot. put a friggin parameter there so people can reuse it. Make it tweakable. And write the tests for pity’s sake; clean code and clarity of thought go together.

At Square we try to maintain reusability and readability — we structure our code in different folders with distinct, reusable components that provide semantics around the different parts of building a machine learning model: model, signal, error, experiment.

We only write scripts in the experiments folder where we either tie together components from model, signal and error or we conduct exploratory data analysis. It’s more than just a script, it’s a way of thinking, a philosophy of approach.

What does such a discipline give you? Every time you run an experiment your should incrementally increase your knowledge. This discipline helps you make sure you don’t do the same work again. Without it you can’t even figure out the things you or someone else has already attempted.

For more on what every project directory should contain, see Project Template, written by John Myles White.

We had a brief discussion of how reading other people’s code is a huge problem, especially when we don’t even know what clean code looks like. Ian stayed firm on his claim that “if you don’t write production code then you’re not productive.”

In this light, Ian suggests exploring and actively reading Github’s repository of R code. He says to try writing your own R package after reading this. Also, he says that developing an aesthetic sense for code is analogous to acquiring the taste for beautiful proofs; it’s done through rigorous practice and feedback from peers and mentors. The problem is, he says, that statistics instructors in schools usually do not give feedback on code quality, nor are they qualified to.

For extra credit, Ian suggests the reader contrasts the implementations of the caret package (poor code) with scikit-learn (clean code).

Important things Ian skipped

• how is a model “productionized”?
• how are features computed in real-time to support these models?
• how do we make sure “what we see is what we get”, meaning the features we build in a training environment will be the ones we see in real-time. Turns out this is a pretty big problem.
• how do you test a risk engine?

Next Ian talked to us about how Square uses visualization.

Data Viz at Square

Ian talked to us about a bunch of different ways the Inference Team at Square use visualizations to monitor the transactions going on at any given time. He mentioned that these monitors aren’t necessarily trying to predict fraud per se but rather provides a way of keeping an eye on things to look for trends and patterns over time and serves as the kind of “data exoskeleton” that he mentioned at the beginning. People at Square believe in ambient analytics, which means passively ingesting data constantly so you develop a visceral feel for it.

After all, it is only by becoming very familiar with our data that we even know what kind of patterns are unusual or deserve their own model. To go further into the philosophy of this approach, he said two thing:

“What gets measured gets managed,” and “You can’t improve what you don’t measure.”

He described a workflow tool to review users, which shows features of the seller, including the history of sales and geographical information, reviews, contact info, and more. Think mission control.

In addition to the raw transactions, there are risk metrics that Ian keeps a close eye on. So for example he monitors the “clear rates” and “freeze rates” per day, as well as how many events needed to be reviewed. Using his fancy viz system he can get down to which analysts froze the most today and how long each account took to review, and what attributes indicate a long review process.

In general people at Square are big believers in visualizing business metrics (sign-ups, activations, active users, etc.) in dashboards; they think it leads to more accountability and better improvement of models as they degrade. They run a kind of constant EKG of their business through ambient analytics.

Ian ended with his data scientist profile. He thinks it should be on a logarithmic scale, since it doesn’t take very long to be okay at something (good enough to get by) but it takes lots of time to get from good to great. He believes that productivity should also be measured in log-scale, and his argument is that leading software contributors crank out packages at a much higher rate than other people.

Ian’s advice to aspiring data scientists

1. play with real data
2. build a good foundation in school
3. get an internship
4. be literate, not just in statistics
5. stay curious

Ian’s thought experiment

Suppose you know about every single transaction in the world as it occurs. How would you use that data?

This week our guest lecturer for the Columbia Data Science class was Brian Dalessandro. Brian works at Media6Degrees as a VP of Data Science, and he’s super active in the research community. He’s also served as co-chair of the KDD competition.

Before Brian started, Rachel threw us a couple of delicious data science tidbits.

The Process of Data Science

First we have the Real World. Inside the Real World we have:

• Users using Google+
• People competing in the Olympics
• Spammers sending email

From this we draw raw data, e.g. logs, all the olympics records, or Enron employee emails. We want to process this to make it clean for analysis. We use pipelines of data munging, joining, scraping, wrangling or whatever you want to call it and we use tools such as:

• python
• shell scripts
• R
• SQL

We eventually get the data down to a nice format, say something with columns:

name event year gender event time

Note: this is where you typically start in a standard statistics class. But it’s not where we typically start in the real world.

Once you have this clean data set, you should be doing some kind of exploratory data analysis (EDA); if you don’t really know what I’m talking about then look at Rachel’s recent blog post on the subject. You may realize that it isn’t actually clean.

Next, you decide to apply some algorithm you learned somewhere:

• k-nearest neighbor
• regression
• Naive Bayes
• (something else),

depending on the type of problem you’re trying to solve:

• classification
• prediction
• description

You then:

• interpret
• visualize
• report
• communicate

At the end you have a “data product”, e.g. a spam classifier.

K-means

So far we’ve only seen supervised learning. K-means is the first unsupervised learning technique we’ll look into. Say you have data at the user level:

• G+ data
• survey data
• medical data
• SAT scores

Assume each row of your data set corresponds to a person, say each row corresponds to information about the user as follows:

age gender income Geo=state household size

Your goal is to segment them, otherwise known as stratify, or group, or cluster. Why? For example:

• you might want to give different users different experiences. Marketing often does this.
• you might have a model that works better for specific groups
• hierarchical modeling in statistics does something like this.

One possibility is to choose the groups yourself. Bucket users using homemade thresholds. Like by age, 20-24, 25-30, etc. or by income. In fact, say you did this, by age, gender, state, income, marital status. You may have 10 age buckets, 2 gender buckets, and so on, which would result in 10x2x50x10x3 = 30,000 possible bins, which is big.

You can picture a five dimensional space with buckets along each axis, and each user would then live in one of those 30,000 five-dimensional cells. You wouldn’t want 30,000 marketing campaigns so you’d have to bin the bins somewhat.

Wait, what if you want to use an algorithm instead where you could decide on the number of bins? K-means is a “clustering algorithm”, and k is the number of groups. You pick k, a hyper parameter.

2-d version

Say you have users with #clicks, #impressions (or age and income – anything with just two numerical parameters). Then k-means looks for clusters on the 2-d plane. Here’s a stolen and simplistic picture that illustrates what this might look like:

The general algorithm is just the same picture but generalized to d dimensions, where d is the number of features for each data point.

Here’s the actual algorithm:

• randomly pick K centroids
• assign data to closest centroid.
• move the centroids to the average location of the users assigned to it
• repeat until the assignments don’t change

It’s up to you to interpret if there’s a natural way to describe these groups.

This is unsupervised learning and it has issues:

• choosing an optimal k is also a problem although , where n is number of data points.
• convergence issues – the solution can fail to exist (the configurations can fall into a loop) or “wrong”
• but it’s also fast
• interpretability can be a problem – sometimes the answer isn’t useful
• in spite of this, there are broad applications in marketing, computer vision (partition an image), or as a starting point for other models.

One common tool we use a lot in our systems is logistic regression.

Thought Experiment

Brian now asked us the following:

How would data science differ if we had a “grand unified theory of everything”?

He gave us some thoughts:

• Would we even need data science?
• Theory offers us a symbolic explanation of how the world works.
• What’s the difference between physics and data science?
• Is it just accuracy? After all, Newton wasn’t completely precise, but was pretty close.

If you think of the sciences as a continuum, where physics is all the way on the right, and as you go left, you get more chaotic, then where is economics on this spectrum? Marketing? Finance? As we go left, we’re adding randomness (and as a clever student points out, salary as well).

Bottomline: if we could model this data science stuff like we know how to model physics, we’d know when people will click on what ad. The real world isn’t this understood, nor do we expect to be able to in the future.

Does “data science” deserve the word “science” in its name? Here’s why maybe the answer is yes.

We always have more than one model, and our models are always changing.

The art in data science is this: translating the problem into the language of data science

The science in data science is this: given raw data, constraints and a problem statement, you have an infinite set of models to choose from, with which you will use to maximize performance on some evaluation metric, that you will have to specify. Every design choice you make can be formulated as an hypothesis, upon which you will use rigorous testing and experimentation to either validate or refute.

Never underestimate the power of creativity: usually people have vision but no method. As the data scientist, you have to turn it into a model within the operational constraints. You need to optimize a metric that you get to define. Moreover, you do this with a scientific method, in the following sense.

Namely, you hold onto your existing best performer, and once you have a new idea to prototype, then you set up an experiment wherein the two best models compete. You therefore have a continuous scientific experiment, and in that sense you can justify it as a science.

Classifiers

Given

• data
• a problem, and
• constraints,

we need to determine:

• a classifier,
• an optimization method,
• a loss function,
• features, and
• an evaluation metric.

Today we will focus on the process of choosing a classifier.

Classification involves mapping your data points into a finite set of labels or the probability of a given label or labels. Examples of when you’d want to use classification:

• will someone click on this ad?
• what number is this?
• what is this news article about?
• is this spam?
• is this pill good for headaches?

From now on we’ll talk about binary classification only (0 or 1).

Examples of classification algorithms:

• decision tree
• random forests
• naive bayes
• k-nearest neighbors
• logistic regression
• support vector machines
• neural networks

Which one should we use?

One possibility is to try them all, and choose the best performer. This is fine if you have no constraints or if you ignore constraints. But usually constraints are a big deal – you might have tons of data or not much time or both.

If I need to update 500 models a day, I do need to care about runtime. these end up being bidding decisions. Some algorithms are slow – k-nearest neighbors for example. Linear models, by contrast, are very fast.

One under-appreciated constraint of a data scientist is this: your own understanding of the algorithm.

Ask yourself carefully, do you understand it for real? Really? Admit it if you don’t. You don’t have to be a master of every algorithm to be a good data scientist. The truth is, getting the “best-fit” of an algorithm often requires intimate knowledge of said algorithm. Sometimes you need to tweak an algorithm to make it fit your data. A common mistake for people not completely familiar with an algorithm is to overfit.

Another common constraint: interpretability. You often need to be able to interpret your model, for the sake of the business for example. Decision trees are very easy to interpret. Random forests, on the other hand, not so much, even though it’s almost the same thing, but can take exponentially longer to explain in full. If you don’t have 15 years to spend understanding a result, you may be willing to give up some accuracy in order to have it easy to understand.

Note that credit cards have to be able to explain their models by law so decision trees make more sense than random forests.

How about scalability? In general, there are three things you have to keep in mind when considering scalability:

• learning time: how much time does it take to train the model?
• scoring time: how much time does it take to give a new user a score once the model is in production?
• model storage: how much memory does the production model use up?

Here’s a useful paper to look at when comparing models: “An Empirical Comparison of Supervised Learning Algorithms”, from which we learn:

• Simpler models are more interpretable but aren’t as good performers.
• The question of which algorithm works best is problem dependent
• It’s also constraint dependent

At M6D, we need to match clients (advertising companies) to individual users. We have logged the sites they have visited on the internet. Different sites collect this information for us. We don’t look at the contents of the page – we take the url and hash it into some random string and then we have, say, the following data about a user we call “u”:

u = <xyz, 123, sdqwe, 13ms>

This means u visited 4 sites and their urls hashed to the above strings. Recall last week we learned spam classifier where the features are words. We aren’t looking at the meaning of the words. So the might as well be strings.

At the end of the day we build a giant matrix whose columns correspond to sites and whose rows correspond to users, and there’s a “1″ if that user went to that site.

To make this a classifier, we also need to associate the behavior “clicked on a shoe ad”. So, a label.

Once we’ve labeled as above, this looks just like spam classification. We can now rely on well-established methods developed for spam classification – reduction to a previously solved problem.

Logistic Regression

We have three core problems as data scientists at M6D:

• feature engineering,
• user level conversion prediction,
• bidding.

We will focus on the second. We use logistic regression- it’s highly scalable and works great for binary outcomes.

What if you wanted to do something else? You could simply find a threshold so that, above you get 1, below you get 0. Or you could use a linear model like linear regression, but then you’d need to cut off below 0 or above 1.

What’s better: fit a function that is bounded in side [0,1]. For example, the logit function

wanna estimate

.

To make this a linear model in the outcomes , we take the log of the odds ratio:

The parameter keeps shape of the logit curve but shifts it back and forth. To interpret further, consider what we call the base rate, the unconditional probability of “1″ (so, in the case of ads, the base rate would correspond to the click-through rate, i.e. the overall tendency for people to click on ads; this is typically on the order of 1%).

If you had no information except the base rate, the average prediction would be just that. In a logistical regression, defines the base rate. Specifically, the base rate is approximately equal to

The slope defines the slope of the logit function. Note in general it’s a vector which is as long as the number of features we are using for each data point.

Our immediate modeling goal is to use our training data to find the best choices for and We will use a maximum likelihood estimation or convex optimization to achieve this; we can’t just use derivatives and vector calculus like we did with linear regression because it’s a complicated function of our data.

The likelihood function is defined by:

where we are assuming the data points are independent and where

We then search for the parameters that maximize this having observed our data:

The probability of a single observation is

where is the modeled probability of a “1″ for the binary outcome $Y_i.$ Taking the product of all of these we get our likelihood function which we want to maximize.

Similar to last week, we now take the log and get something convex, so it has to have a global maximum. Finally, we use numerical techniques to find it, which essentially follow the gradient like Newton’s method from calculus. Computer programs can do this pretty well. These algorithms depend on a step size, which we will need to adjust as we get closer to the global max or min – there’s an art to this piece of numerical optimization as well. Each step of the algorithm looks something like this:

where remember we are actually optimizing our parameters and to maximize the (log) likelihood function, so the you see above is really a vector of s and the function corresponds to our

“Flavors” of Logistic Regression for convex optimization.

The Newton’s method we described above is also called Iterative Reweighted Least Squares. It uses the curvature of log-likelihood to choose appropriate step direction. The actual calculation involves the Hessian matrix, and in particular requires its inversion, which is a kxk matrix. This is bad when there’s lots of features, as in 10,000 or something. Typically we don’t have that many features but it’s not impossible.

Another possible method to maximize our likelihood or log likelihood is called Stochastic Gradient Descent. It approximates gradient using a single observation at a time. The algorithm updates the current best-fit parameters each time it sees a new data point. The good news is that there’s no big matrix inversion, and it works well with huge data and with sparse features; it’s a big deal in Mahout and Vowpal Wabbit. The bad news is it’s not such a great optimizer and it’s very dependent on step size.

Evaluation

We generally use different evaluation metrics for different kind of models.

First, for ranking models, where we just want to know a relative rank versus and absolute score, we’d look to one of:

• area under the receiver operating curve (AUC)
• area under the cumulative lift curve

Second, for classification models, we’d look at the following metrics:

• lift: how much more people are buying or clicking because of a model
• accuracy: how often the correct outcome is being predicted
• f-score
• precision
• recall

Finally, for density estimation, where we need to know an actual probability rather than a relative score, we’d look to:

• mean absolute error
• mean squared error

In general it’s hard to compare lift curves but you can compare AUC (area under the receiver operator curve) – they are “base rate invariant.” In other words if you bring the click-through rate from 1% to 2%, that’s 100% lift but if you bring it from 4% to 7% that’s less lift but more effect. AUC does a better job in such a situation when you want to compare.

Density estimation tests tell you how well are you fitting for conditional probability. In advertising, this may arise if you have a situation where each ad impression costs $c and for each conversion you receive $q. You will want to target every conversion that has a positive expected value, i.e. whenever

But to do this you need to make sure the probability estimate on the left is accurate, which in this case means something like the mean squared error of the estimator is small. Note a model can give you good rankings but bad P estimates.

Similarly, features that rank highly on AUC don’t necessarily rank well with respect to mean absolute error. So feature selection, as well as your evaluation method, is completely context-driven.

In the third week of the Columbia Data Science course, our guest lecturer was Jake Hofman. Jake is at Microsoft Research after recently leaving Yahoo! Research. He got a Ph.D. in physics at Columbia and taught a fantastic course on modeling last semester at Columbia.

After introducing himself, Jake drew up his “data science profile;” turns out he is an expert on a category that he created called “data wrangling.” He confesses that he doesn’t know if he spends so much time on it because he’s good at it or because he’s bad at it.

Thought Experiment: Learning by Example

Jake had us look at a bunch of text. What is it? After some time we describe each row as the subject and first line of an email in Jake’s inbox. We notice the bottom half of the rows of text looks like spam.

Now Jake asks us, how did you figure this out? Can you write code to automate the spam filter that your brain is?

Some ideas the students came up with:

• Any email is spam if it contains Viagra references. Jake: this will work if they don’t modify the word.
• Maybe something about the length of the subject?
• Exclamation points may point to spam. Jake: can’t just do that since “Yahoo!” would count.
• Jake: keep in mind spammers are smart. As soon as you make a move, they game your model. It would be great if we could get them to solve important problems.
• Should we use a probabilistic model? Jake: yes, that’s where we’re going.
• Should we use k-nearest neighbors? Should we use regression? Recall we learned about these techniques last week. Jake: neither. We’ll use Naive Bayes, which is somehow between the two.

Why is linear regression not going to work?

Say you make a feature for each lower case word that you see in any email and then we used R’s “lm function:”

lm(spam ~ word1 + word2 + …)

Wait, that’s too many variables compared to observations! We have on the order of 10,000 emails with on the order of 100,000 words. This will definitely overfit. Technically, this corresponds to the fact that the matrix in the equation for linear regression is not invertible. Moreover, maybe can’t even store it because it’s so huge.

Maybe you could limit to top 10,000 words? Even so, that’s too many variables vs. observations to feel good about it.

Another thing to consider is that target is 0 or 1 (0 if not spam, 1 if spam), whereas you wouldn’t get a 0 or a 1 in actuality through using linear regression, you’d get a number. Of course you could choose a critical value so that above that we call it “1″ and below we call it “0″. Next week we’ll do even better when we explore logistic regression, which is set up to model a binary response like this.

How about k-nearest neighbors?

To use k-nearest neighbors we would still need to choose features, probably corresponding to words, and you’d likely define the value of those features to be 0 or 1 depending on whether the word is present or not. This leads to a weird notion of “nearness”.

Again, with 10,000 emails and 100,000 words, we’ll encounter a problem: it’s not a singular matrix this time but rather that the space we’d be working in has too many dimensions. This means that, for example, it requires lots of computational work to even compute distances, but even that’s not the real problem.

The real problem is even more basic: even your nearest neighbors are really far away. this is called “the curse of dimensionality“. This problem makes for a poor algorithm.

Question: what if sharing a bunch of words doesn’t mean sentences are near each other in the sense of language? I can imagine two sentences with the same words but very different meanings.

Jake: it’s not as bad as it sounds like it might be – I’ll give you references at the end that partly explain why.

Aside: digit recognition

In this case k-nearest neighbors works well and moreover you can write it in a few lines of R.

Take your underlying representation apart pixel by pixel, say in a 16 x 16 grid of pixels, and measure how bright each pixel is. Unwrap the 16×16 grid and put it into a 256-dimensional space, which has a natural archimedean metric. Now apply the k-nearest neighbors algorithm.

Some notes:

• If you vary the number of neighbors, it changes the shape of the boundary and you can tune k to prevent overfitting.
• You can get 97% accuracy with a sufficiently large data set.
• Result can be viewed in a “confusion matrix“.

Naive Bayes

Question: You’re testing for a rare disease, with 1% of the population is infected. You have a highly sensitive and specific test:

• 99% of sick patients test positive
• 99% of healthy patients test negative

Given that a patient tests positive, what is the probability that the patient is actually sick?

Answer: Imagine you have 100×100 = 10,000 people. 100 are sick, 9,900 are healthy. 99 sick people test sick, and 99 healthy people do too. So if you test positive, you’re equally likely to be healthy or sick. So the answer is 50%.

Let’s do it again using fancy notation so we’ll feel smart:

Recall

and solve for

The denominator can be thought of as a “normalization constant;” we will often be able to avoid explicitly calculuating this. When we apply the above to our situation, we get:

This is called “Bayes’ Rule“. How do we use Bayes’ Rule to create a good spam filter? Think about it this way: if the word “Viagra” appears, this adds to the probability that the email is spam.

To see how this will work we will first focus on just one word at a time, which we generically call “word”. Then we have:

The right-hand side of the above is computable using enough pre-labeled data. If we refer to non-spam as “ham”, we only need and This is essentially a counting exercise.

Example: go online and download Enron emails. Awesome. We are building a spam filter on that – really this means we’re building a new spam filter on top of the spam filter that existed for the employees of Enron.

Jake has a quick and dirty shell script in bash which runs this. It downloads and unzips file, creates a folder. Each text file is an email. They put spam and ham in separate folders.

Jake uses “wc” to count the number of messages for one former Enron employee, for example. He sees 1500 spam, and 3672 ham. Using grep, he counts the number of instances of “meeting”:

grep -il meeting enron1/spam/*.txt | wc -l

This gives 153. This is one of the handful of computations we need to compute

Note we don’t need a fancy programming environment to get this done.

Next, we try:

• “money”: 80% chance of being spam.
• “viagra”: 100% chance.
• “enron”: 0% chance.

This illustrates overfitting; we are getting overconfident because of our biased data. It’s possible, in other words, to write an non-spam email with the word “viagra” as well as a spam email with the word “enron.”

Next, do it for all the words. Each document can be represented by a binary vector, whose jth entry is 1 or 0 depending whether jth word appears. Note this is a huge-ass vector, we will probably actually represent it with the indices of the words that actually do show up.

Here’s the model we use to estimate the probability that we’d see a given word vector given that we know it’s spam (or that it’s ham). We denote the document vector and the various entries , where the correspond to all the indices of in other words over all the words. For now we denote “is spam” by :

The theta here is the probability that an individual word is present in a spam email (we can assume separately and parallel-ly compute that for every word). Note we are modeling the words independently and we don’t count how many times they are present. That’s why this is called “Naive”.

Let’s take the log of both sides:

[It's good to take the log because multiplying together tiny numbers can give us numerical problems.]

The term doesn’t depend on a given document, just the word, so let’s rename it Same with . The real weights that vary by document are the ‘s.

We can now use Bayes’ Rule to get an estimate of which is what we actually want. We can also get away with not computing all the terms if we only care whether it’s more likely to be spam or to be ham. Only the varying term needs to be computed.

Wait, this ends up looking like a linear regression! But instead of computing them by inverting a huge matrix, the weights come from the Naive Bayes’ algorithm.

This algorithm works pretty well and it’s “cheap to train” if you have pre-labeled data set to train on. Given a ton of emails, just count the words in spam and non-spam emails. If you get more training data you can easily increment your counts. In practice there’s a global model, which you personalize to individuals. Moreover, there are lots of hard-coded, cheap rules before an email gets put into a fancy and slow model.

Here are some references:

• “Idiot’s Bayes – not so stupid after all?” – the whole paper is about why it doesn’t suck, which is related to redundancies in language.
• “Naive Bayes at Forty: The Independence Assumption in Information“
• “Spam Filtering with Naive Bayes – Which Naive Bayes?“

Laplace Smoothing

Laplace Smoothing refers to the idea of replacing our straight-up estimate of the probability of seeing a given word in a spam email with something a bit fancier:

We might fix and for example, to prevents the possibility of getting 0 or 1 for a probability. Does this seem totally ad hoc? Well if we want to get fancy, we can see this as equivalent to having a prior and performing a maximal likelihood estimate.

If we denote by the maximal likelihood estimate, then we have:

In other words, we are asking the question, for what value of were the data D most probable? If we assume independent trials then we want to maximize

If you take the derivative, and set it to zero, we get

In other words, just what we had before. Now let’s add a prior. Denote by the maximum a posteriori likelihood:

This similarly asks the question, given the data I saw, which parameter is the most likely?

Use Bayes’ rule to get . This looks similar to above except for the , which is the “prior”. If I assume is of the form ; then we get the above, Laplacian smoothed version.

Sometimes and are called “pseudo counts”. They’re fancy but also simple. It’s up to the data scientist to set the values of these hyperparameters, and it gives us two knobs to tune. By contrast, k-nearest neighbors has one knob, namely k.

Note: In the last 5 years people have started using stochastic gradient methods to avoid the non-invertible (overfitting) matrix problem. Switching to logistic regression with stochastic gradient method helped a lot, and can account for correlations between words. Even so, Naive Bayes’ is pretty impressively good considering how simple it is.

Scraping the web: API’s

For the sake of this discussion, an API (application programming interface) is something websites provide to developers so they can download data from the website easily and in standard format. Usually the developer has to register and receive a “key”, which is something like a password. For example, the New York Times has an API here. Note that some websites limit what data you have access to through their API’s or how often you can ask for data without paying for it.

When you go this route, you often get back weird formats, sometimes in JSON, but there’s no standardization to this standardization, i.e. different websites give you different “standard” formats.

One way to get beyond this is to use Yahoo’s YQL language which allows you to go to the Yahoo! Developer Network and write SQL-like queries that interact with many of the common API’s on the common sites like this:

select * from flickr.photos.search where text=”Cat” and api_key=”lksdjflskjdfsldkfj” limit 10

The output is standard and I only have to parse this in python once.

What if you want data when there’s no API available?

Note: always check the terms and services of the website before scraping.

In this case you might want to use something like the Firebug extension for Firefox, you can “inspect the element” on any webpage, and Firebug allows you to grab the field inside the html. In fact it gives you access to the full html document so you can interact and edit. In this way you can see the html as a map of the page and Firebug is a kind of tourguide.

After locating the stuff you want inside the html, you can use curl, wget, grep, awk, perl, etc., to write a quick and dirty shell script to grab what you want, especially for a one-off grab. If you want to be more systematic you can also do this using python or R.

Other parsing tools you might want to look into:

• lynx and lynx –dump: good if you pine for the 1970′s. Oh wait, 1992. Whatever.
• Beautiful Soup: robust but kind of slow
• Mechanize (or here) super cool as well but doesn’t parse javascript.

Postscript: Image Classification

How do you determine if an image is a landscape or a headshot?

You either need to get someone to label these things, which is a lot of work, or you can grab lots of pictures from flickr and ask for photos that have already been tagged.

Represent each image with a binned RGB – (red green blue) intensity histogram. In other words, for each pixel, for each of red, green, and blue, which are the basic colors in pixels, you measure the intensity, which is a number between 0 and 255.

Then draw three histograms, one for each basic color, showing us how many pixels had which intensity. It’s better to do a binned histogram, so have counts of # pixels of intensity 0 – 51, etc. – in the end, for each picture, you have 15 numbers, corresponding to 3 colors and 5 bins per color. We are assuming every picture has the same number of pixels here.

Finally, use k-nearest neighbors to decide how much “blue” makes a landscape versus a headshot. We can tune the hyperparameters, which in this case are # of bins as well as k.