Machine Learning (Theory)


Randomized experimentation

One good thing about doing machine learning at present is that people actually use it! The back-ends of many systems we interact with on a daily basis are driven by machine learning. In most such systems, as users interact with the system, it is natural for the system designer to wish to optimize the models under the hood over time, in a way that improves the user experience. To ground the discussion a bit, let us consider the example of an online portal, that is trying to present interesting news stories to its user. A user comes to the portal and based on whatever information the portal has on the user, it recommends one (or more) news stories. The user chooses to read the story or not and life goes on. Naturally the portal wants to better tailor the stories it displays to the users’ taste over time, which can be observed if users start to click on the displayed story more often.

A natural idea would be to use the past logs and train a machine learning model which prefers the stories that users click on and discourages the stories which are avoided by the users. This sounds like a simple classification problem, for which we might use an off-the-shelf algorithm. This is indeed done reasonably often, and the offline logs suggest that the newly trained model will result in a lot more clicks than the old one. The old model is deployed, only to find out its performance is not as good as hoped, or even poorer than what was happening before! What went wrong? The natural reaction is typically that (a) the machine learning algorithm needs to be improved, or (b) we need better features, or (c) we need more data. Alas, in most of these cases, the right answer is (d) none of the above. Let us see why this is true through a simple example.

Imagine a simple world where some of our users are from New York and others are from Seattle. Some of our news stories pertain to finance, and others pertain to technology. Let us further imagine that the probability of a click (henceforth CTR for clickthrough rate) on a news article based on city and subject has the following distribution:


Finance CTR

Tech CTR

New York 1 0.6
Seattle 0.4 0.79

Table1: True (unobserved) CTRs

Of course, we do not have this information ahead of time while designing the system, so our starting system recommends articles according to some heuristic rule. Imagine that we user the rule:

  • New York users get Tech stories, Seattle users get Finance stories.

Now we collect the click data according to this system for a while. As we obtain more and more data, we obtain increasingly accurate estimates of the CTR for Tech stories and NY users, as well as Finance stories and Seattle users (0.6 and 0.4 resp.). However, we have no information on the other two combinations. So if we train a machine learning algorithm to minimize the squared loss between predicted CTR on an article and observed CTR, it is likely to predict the average of observed CTRs (that is 0.5) in the other two blocks. At this point, our guess looks like:



Finance CTR

Tech CTR

New York 1 / ? / 0.5 0.6 / 0.6 / 0.6
Seattle 0.4 / 0.4 / 0.4 0.79 / ? / 0.5

Table2: True / observed / estimated CTRs

Note that this would be the case even with infinite data and an all powerful learner, so machine learning is not to be faulted in any way here. Given these estimates, we naturally realize that show finance articles to Seattle users was a mistake, and switch to Tech. But Tech is also looking pretty good in NY, and we stick with it. Our new policy is:

  • Both NY and Seattle users get Tech articles.

Running the new system for a while, we will fix the erroneous estimates for the Tech CTR on Seattle (that is, up 0.5 to 0.79). But we still have no signal that makes us prefer Finance over Tech in NY. Indeed even with infinite data, the system will be stuck with this suboptimal choice at this point, and our CTR estimates will look something like:


Finance CTR

Tech CTR

New York 1 / ? / 0.59 0.6 / 0.6 / 0.6
Seattle 0.4 / 0.4 / 0.4 0.79 / 0.79 / 0.79

Table3: True / observed / estimated CTRs

We can now assess the earlier claims:

  1. More data does not help: Since Observed and True CTRs match wherever we are collecting data
  2. Better learning algorithm does not help: Since Predicted and Observed CTRs coincide wherever we are collecting data
  3. Better data does help!! We should not be having the blank cell in observed column.

This seems simple enough to fix though. We should have really known better than to completely omit observations in one cell of our table. With good intentions, we decide to collect data in all cells. We choose to use the following rule:

  • Seattle users get Tech stories during day and finance stories during night
  • Similarly, NY users get Tech stories during day and finance stories during night

We are now collecting data on each cell, but we find that our estimates still lead us to a suboptimal policy. Further investigation might reveal that users are more likely to read finance stories during the day when the markets are open. So when we only display finance stories during night, we underestimate the finance CTR and end up with wrong estimates. Realizing the error of our ways, we might try to fix this again and then run into another problem and so on.

The issue we have discovered above is that of confounding variables. There is lot of wonderful work and many techniques that can be used to circumvent confounding variables in experimentation. Here, I mention the simplest one and perhaps the most versatile one of them: Randomization. The idea is that instead of recommending stories to users according to a fix deterministic rule, we allow for different articles to be presented to the user according to some distribution. This distribution does not have to be uniform. In fact, good randomization would likely focus on plausibly good articles so as to not degrade the user experience. However, as long as we add sufficient randomization, we can then obtain consistent counterfactual estimates of quantities from our experimental data. There is growing literature on how to do this well. A nice paper which covers some of these techniques and provides an empirical evaluation is A more involved example in the context of computational advertising at Microsoft is discussed in




Conference on Digitial Experimentation

I just attended CODE. The set of people interested in digital experimentation have very diverse backgrounds encompassing theory, machine learning, social science, economics, and industry so this seems like a good subject for a new conference. I hope it continues.

I found several talks interesting.

  • Eytan Bakshy talked about PlanOut which is language/platform for flexibly specifying experiments.
  • Ron Kohavi talked about EXP which is a heavily used A/B testing platform.
  • Susan Athey talked about long term vs short term metrics which seems both important to address, a constant problem, and not yet systematically solved.

There was a panel about the ongoing Facebook experimentation controversy. The issue here is complex. My understanding is that Facebook users have some expected ownership of the content they create, and hence aren’t comfortable with the content being used in unexpected ways. On the other hand, experimentation is so necessary to the functioning of all large modern internet sites that banning it or slowing down the process by a factor of a million (as some advocated) would badly degrade the future of these sites in practice.

My belief is that what’s lacking is education and trust. W.r.t. education, people need to understand that experimentation is unavoidable when trying to figure out how to optimize an enormously complex system, as there is just no other way to systematically make 1000 right decisions as is necessary for basic things like choosing the best homepage/search result/etc… W.r.t. trust, companies are not particularly good at creating trust in general, but finding the right mechanism for doing so seems critical. I would point out Vanguard as a company that managed to successfully create trust by design.


Vowpal Wabbit, version 7.0

A new version of VW is out. The primary changes are:

  1. Learning Reductions: I’ve wanted to get learning reductions working and we’ve finally done it. Not everything is implemented yet, but VW now supports direct:
    1. Multiclass Classification –oaa or –ect.
    2. Cost Sensitive Multiclass Classification –csoaa or –wap.
    3. Contextual Bandit Classification –cb.
    4. Sequential Structured Prediction –searn or –dagger

    In addition, it is now easy to build your own custom learning reductions for various plausible uses: feature diddling, custom structured prediction problems, or alternate learning reductions. This effort is far from done, but it is now in a generally useful state. Note that all learning reductions inherit the ability to do cluster parallel learning.

  2. Library interface: VW now has a basic library interface. The library provides most of the functionality of VW, with the limitation that it is monolithic and nonreentrant. These will be improved over time.
  3. Windows port: The priority of a windows port jumped way up once we moved to Microsoft. The only feature which we know doesn’t work at present is automatic backgrounding when in daemon mode.
  4. New update rule: Stephane visited us this summer, and we fixed the default online update rule so that it is unit invariant.

There are also many other small updates including some contributed utilities that aid the process of applying and using VW.

Plans for the near future involve improving the quality of various items above, and of course better documentation: several of the reductions are not yet well documented.


KDD and MUCMD 2011

At KDD I enjoyed Stephen Boyd‘s invited talk about optimization quite a bit. However, the most interesting talk for me was David Haussler‘s. His talk started out with a formidable load of biological complexity. About half-way through you start wondering, “can this be used to help with cancer?” And at the end he connects it directly to use with a call to arms for the audience: cure cancer. The core thesis here is that cancer is a complex set of diseases which can be distentangled via genetic assays, allowing attacking the specific signature of individual cancers. However, the data quantity and complex dependencies within the data require systematic and relatively automatic prediction and analysis algorithms of the kind that we are best familiar with.

Some of the papers which interested me are:

  1. Kai-Wei Chang and Dan Roth, Selective Block Minimization for Faster Convergence of Limited Memory Large-Scale Linear Models, which is about effectively using a hard-example cache to speedup learning.
  2. Leland Wilkinson, Anushka Anand, and Dang Nhon Tuan, CHIRP: A New Classifier Based on Composite Hypercubes on Iterated Random Projections. The bar on creating new classifiers is pretty high. The approach here uses a combination of random projection and partition which appears to be compelling for some nonlinear and relatively high computation settings. They do a more thorough empirical evaluation than most papers.
  3. Zhuang Wang, Nemanja Djuric, Koby Crammer, and Slobodan Vucetic Trading Representability for Scalability: Adaptive Multi-Hyperplane Machine for Nonlinear Classification. The paper explores an interesting idea: having lots of weight vectors (effectively infinity) associated with a particular label, showing that algorithms on this representation can deal with lots of data as per linear predictors, but with superior-to-linear performance. The authors don’t use the hashing trick, but their representation is begging for it.
  4. Michael Bruckner and Tobias Scheffer, Stackelberg Games for Adversarial Prediction Problem. This is about email spam filtering, where the authors use a theory of adversarial equilibria to construct a more robust filter, at least in some cases. Demonstrating this on noninteractive data is inherently difficult.

There were also three papers that were about creating (or perhaps composing) learning systems to do something cool.

  1. Gideon Dror, Yehuda Koren, Yoelle Maarek, and Idan Szpektor, I Want to Answer, Who Has a Question? Yahoo! Answers Recommender System. This is about how to learn to route a question to the appropriate answerer automatically.
  2. Yehuda Koren, Edo Liberty, Yoelle Maarek, and Roman Sandler, Automatically Tagging Email by Leveraging Other Users’ Folders. This is about helping people organize their email with machine learning.
  3. D. Sculley, Matthew Eric Otey, Michael Pohl, Bridget Spitznagel, John Hainsworth, Yunkai Zhou, Detecting Adversarial Advertisements in the Wild. The title is an excellent abstract here, and there are quite a few details about the implementation.

I also attended MUCMD, a workshop on the Meaningful Use of Complex Medical Data shortly afterwards. This workshop is about the emergent area of using data to improve medicine. The combination of electronic health records, the economic importance of getting medicine right, and the relatively weak use of existing data implies there is much good work to do.

This finally gave us a chance to discuss radically superior medical trial designs based on work in exploration and learning :)

Jeff Hammerbacher‘s talk was a hilarilously blunt and well stated monologue about the need and how to gather data in a usable way.

Amongst the talks on using medical data, Suchi Saria‘s seemed the most mature. They’ve constructed a noninvasive test for problem infants which is radically superior to the existing Apgar score according to leave-one-out cross validation.

From the doctor’s side, there was discussion of the deep balkanization of data systems within hospitals, efforts to overcome that, and the (un)trustworthiness of data. Many issues clearly remain here, but it also looks like serious progress is being made.

Overall, the workshop went well, with the broad cross-section of talks providing quite a bit of extra context you don’t normally see. It left me believing that a community centered on MUCMD is rising now, with attendant workshops, conferences, etc… to be expected.


Regretting the dead

Nikos pointed out this new york times article about poor clinical design killing people. For those of us who study learning from exploration information this is a reminder that low regret algorithms are particularly important, as regret in clinical trials is measured by patient deaths.

Two obvious improvements on the experimental design are:

  1. With reasonable record keeping of existing outcomes for the standard treatments, there is no need to explicitly assign people to a control group with the standard treatment, as that approach is effectively explored with great certainty. Asserting otherwise would imply that the nature of effective treatments for cancer has changed between now and a year ago, which denies the value of any clinical trial.
  2. An optimal experimental design will smoothly phase between exploration and exploitation as evidence for a new treatment shows that it can be effective. This is old tech, for example in the EXP3.P algorithm (page 12 aka 59) although I prefer the generalized and somewhat clearer analysis of EXP4.P.

Done the right way, the clinical trial for a successful treatment would start with some initial small pool (equivalent to “phase 1″ in the article) and then simply expanded the pool of participants over time as it proved superior to the existing treatment, until the pool is everyone. And as a bonus, you can even compete with policies on treatments rather than raw treatments (i.e. personalized medicine).

Getting from here to there seems difficult. It’s been 15 years since EXP3.P was first published, and the progress in clinical trial design seems glacial to us outsiders. Partly, I think this is a communication and education failure, but partly, it’s also a failure of imagination within our own field. When we design algorithms, we often don’t think about all the applications, where a little massaging of the design in obvious-to-us ways so as to suit these applications would go a long ways. Getting this right here has a substantial moral aspect, potentially saving millions of lives over time through more precise and fast deployments of new treatments.

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