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COLT Treasurer is now Phil Long

For about 5 years, I’ve been the treasurer of the Association for Computational Learning, otherwise known as COLT, taking over from John Case before me. A transfer of duties to Phil Long is now about complete. This probably matters to almost no one, but I wanted to describe things a bit for those interested.

The immediate impetus for this decision was unhappiness over reviewing decisions at COLT 2009, one as an author and several as a member of the program committee. I seem to have disagreements fairly often about what is important work, partly because I’m focused on learning theory with practical implications, partly because I define learning theory more broadly than is typical amongst COLT members, and partly because COLT suffers a bit from insider-clique issues. The degree to which these issues come up varies substantially each year so last year is not predictive of this one. And, it’s important to understand that COLT remains healthy with these issues not nearly so bad as they were. Nevertheless, I would like to see them taken more actively into account than I’ve been able to persuade people so far.

After thinking about it for a few days before acting, I decided to go ahead with the transfer for another reason: I’ve been suffering from multitask poisoning. Partly this is Ada, but partly it’s many other things, each of which takes a small bit of my time, in aggregate leaving me disappointing people, myself in particular. The effect of this has been quite obvious in terms of the posting rate on hunch.net.

Fortunately, Phil Long was ready to take up the duties, and he’s well positioned to do so.

Despite the above, I found being treasurer not particularly difficult. The functions of the treasury part of ACL have been

  1. Self-insurance for the conference each year. Prior to the formation of ACL-the-nonprofit (which Bob was instrumental in), COLT used to buy insurance against the possibility that some disaster would strike canceling the conference while leaving the local organizer on the hook for substantial expenses. When I came in, the treasury was a little bit low for this function, and when I left, somewhat too high.
  2. Budget fragmentation avoidance. Local organizers typically have a local account from which they spend for expenses and collect registration fees. Without the ACL, dealing with net positive or negative local accounts from year to year was awkward. With the ACL, it’s easy to square things up at the end of each year.
  3. A stable point of contact for funding related things. COLT is partly sponsored by several big CS-related companies including IBM, Microsoft, and Google. Providing a stable point of contact definitely helps ease this process. This also helps on the publishing side, where Omnipress is the current publisher of proceedings.
  4. Budget advice for local organizers. Somewhat to my surprise, the proper role of the treasurer was typically asking the local organizer to reduce registration fees rather than increase. The essential observation is that local organizers, because they operate out of a local account, tend to be a bit conservative in budget estimates. On the other hand, because ACL has an adequate interest bearing account, we should expect and desire to spend the interest in each typical year. In effect, ACL is naturally in a position to sponsor COLT to a small but nontrivial degree.

After having been treasurer for a little while, I’m convinced that having a nonprofit to back a conference is a good idea easing many difficulties with relatively small effort.

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A Variance only Deviation Bound

At the PAC-Bayes workshop earlier this week, Olivier Catoni described a result that I hadn’t believed was possible: a deviation bound depending only on the variance of a random variable.

For people not familiar with deviation bounds, this may be hard to appreciate. Deviation bounds, are one of the core components for the foundations of machine learning theory, so developments here have a potential to alter our understanding of how to learn and what is learnable. My understanding is that the basic proof techniques started with Bernstein and have evolved into several variants specialized for various applications. All of the variants I knew had a dependence on the range, with some also having a dependence on the variance of an IID or martingale random variable. This one is the first I know of with a dependence on only the variance.

The basic idea is to use a biased estimator of the mean which is not influenced much by outliers. Then, a deviation bound can be proved by using the exponential moment method, with the sum of the bias and the deviation bounded. The use of a biased estimator is clearly necessary, because an unbiased empirical average is inherently unstable—which was precisely the reason I didn’t think this was possible.

Precisely how this is useful for machine learning isn’t clear yet, but it opens up possibilities. For example, it’s common to suffer from large ranges in exploration settings, such as contextual bandits or active learning.

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The Efficient Robust Conditional Probability Estimation Problem

I’m offering a reward of $1000 for a solution to this problem. This joins the cross validation problem which I’m offering a $500 reward for. I believe both of these problems are hard but plausibly solvable, and plausibly with a solution of substantial practical value. While it’s unlikely these rewards are worth your time on an hourly wage basis, the recognition for solving them definitely should be 🙂

The Problem

The problem is finding a general, robust, and efficient mechanism for estimating a conditional probability P(y|x) where robustness and efficiency are measured using techniques from learning reductions.

In particular, suppose we have access to a binary regression oracle B which has two interfaces—one for specifying training information and one for testing. Training information is specified as B(x’,y’) where x’ is a feature vector and y’ is a scalar in [0,1] with no value returned. Testing is done according to B(x’) with a value in [0,1] returned.

A learning reduction consists of two algorithms R and R-1 which transform examples from the original input problem into examples for the oracle and then transform the oracle’s predictions into a prediction for the original problem.

The algorithm R takes as input a single example (x,y) where x is an feature vector and y is a discrete variable taking values in {1,…,k}. R then specifies a training example (x’,y’) for the oracle B. R can then create another training example for B based on all available information. This process repeats some finite number of times before halting without returning information.

A basic observation is that for any oracle algorithm, a distribution D(x,y) over multiclass examples and a reduction R induces a distribution over a sequence (x’,y’)* of oracle examples. We collapse this into a distribution D'(x’,y’) over oracle examples by drawing uniformly from the sequence.

The algorithm R-1 takes as input a single example (x,y) and returns a value in [0,1] after using (only) the testing interface of B zero or more times.

We measure the power of an oracle and a reduction according to squared-loss regret. In particular we have:


reg(D,R-1)=E(x,y)~ D[(R-1(x,y)-D(y|x))2]

and similarly letting mx’=E(x’,y’)~ D’[y’].

reg(D’,B)=E(x’,y’)~ D’(B(x’) – mx’)2

The open problem is to specify R and R-1 satisfying the following theorem:

For all multiclass distributions D(x,y), for all binary oracles B: The computational complexity of R and R-1 are O(log k)
and


reg(D,R-1) < = C reg(D’,B)

where C is a universal constant.

Alternatively, this open problem is satisfied by proving there exists no deterministic algorithms R,R-1 satisfying the above theorem statement.

Motivation

The problem of conditional probability estimation is endemic to machine learning applications. In fact, in some branches of machine learning, this is simply considered “the problem”. Typically conditional probability estimation is done in situations where the conditional probability of only one bit is required, however there are a growing number of applications where a well-estimated conditional probability over a more complex object is required. For example, all known methods for solving general contextual bandit problems require knowledge of or good estimation of P(a | x) where a is an action.

There is a second intrinsic motivation which is matching the lower bound. No method faster than O(log k) can be imagined because the label y requires log2 k bits to specify and hence read. Similarly it’s easy to prove no learning reduction can provide a regret ratio with C<1.

The motivation for using the learning reduction framework to specify this problem is a combination of generality and the empirical effectiveness in application of learning reductions. Any solution to this will be general because any oracle B can be plugged in, even ones which use many strange kinds of prior information, features, and active multitask hierachical (insert your favorite adjective here) structure.

Related Results

The state of the art is summarized here which shows it’s possible to have a learning reduction satisfying the above theorem with either:

  1. C replaced by (log2 k)2 (using a binary tree structure)
  2. or the computational time increased to O(k) (using an error correcting code structure).

Hence, answering this open problem in the negative shows that there is an inherent computation vs. robustness tradeoff.

There are two other closely related problems, where similar analysis can be done.

  1. For multiclass classification, where the goal is predicting the most likely class, a result analogous to the open problem is provable using error correcting tournaments.
  2. For multiclass classification in a partial label setting, no learning reduction can provide a constant regret guarantee.

Silly tricks that don’t work

Because Learning reductions are not familiar to everyone, It’s helpful to note certain tricks which do not work here to prevent false leads and provide some intuition.

Ignore B‘s predictions and use your favorite learning algorithm instead.

This doesn’t work, because the quantification is for all D. Any specified learning algorithm will have some D on which it has nonzero regret. On the other hand, because R calls the oracle at least once, there is a defined induced distribution D’. Since the theorem must hold for all D and B, it must hold for a D your specified learning algorithm fails on and for a B for which reg(D’,B)=0 implying the theorem is not satisfied.

Feed random examples into B and vacuously satisfy the theorem by making sure that the right hand side is larger than a constant.

This doesn’t work because the theorem is stated in terms of squared loss regret rather than squared loss. In particular, if the oracle is given examples of the form (x’,y’) where y’ is uniformly at random either 0 or 1, any oracle specifying B(x’)=0.5 has zero regret.

Feed pseudorandom examples into B and vacuously satisfy the theorem by making sure that the right hand side is larger than a constant.

This doesn’t work, because the quantification is “for all binary oracles B”, and there exists one which, knowing the pseudorandom seed, can achieve zero loss (and hence zero regret).

Just use Boosting to drive the LHS to zero.

Boosting theorems require a stronger oracle—one which provides an edge over some constant baseline for each invocation. The oracle here is not limited in this fashion since it could completely err for a small fraction of invocations.

Take an existing structure, parameterize it, randomize over the parameterization, and then average over the random elements.

Employing this approach is not straightforward, because the average in D’ is over an increased number of oracle examples. Hence, at a fixed expected (over oracle examples) regret, the number of examples allowed to have a large regret is increased.

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Netflix Challenge 2 Canceled

The second Netflix prize is canceled due to privacy problems. I continue to believe my original assessment of this paper, that the privacy break was somewhat overstated. I still haven’t seen any serious privacy failures on the scale of the AOL search log release.

I expect privacy concerns to continue to be a big issue when dealing with data releases by companies or governments. The theory of maintaining privacy while using data is improving, but it is not yet in a state where the limits of what’s possible are clear let alone how to achieve these limits in a manner friendly to a prediction competition.

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Yahoo! ML events

Yahoo! is sponsoring two machine learning events that might interest people.

  1. The Key Scientific Challenges program (due March 5) for Machine Learning and Statistics offers $5K (plus bonuses) for graduate students working on a core problem of interest to Y! If you are already working on one of these problems, there is no reason not to submit, and if you aren’t you might want to think about it for next year, as I am confident they all press the boundary of the possible in Machine Learning. There are 7 days left.
  2. The Learning to Rank challenge (due May 31) offers an $8K first prize for the best ranking algorithm on a real (and really used) dataset for search ranking, with presentations at an ICML workshop. Unlike the Netflix competition, there are prizes for 2nd, 3rd, and 4th place, perhaps avoiding the heartbreak the ensemble encountered. If you think you know how to rank, you should give it a try, and we might all learn something. There are 3 months left.