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Languages of Learning

A language is a set of primitives which can be combined to succesfully create complex objects. Languages arise in all sorts of situations: mechanical construction, martial arts, communication, etc… Languages appear to be the key to succesfully creating complex objects—it is difficult to come up with any convincing example of a complex object which is not built using some language. Since languages are so crucial to success, it is interesting to organize various machine learning research programs by language.

The most common language in machine learning are languages for representing the solution to machine learning. This includes:

  1. Bayes Nets and Graphical Models A language for representing probability distributions. The key concept supporting modularity is conditional independence. Michael Kearns has been working on extending this to game theory.
  2. Kernelized Linear Classifiers A language for representing linear separators, possibly in a large space. The key form of modularity here is kernelization.
  3. Neural Networks A language for representing and learning functions. The key concept supporting modularity is backpropagation. (Yann LeCun gave some very impressive demos at the Chicago MLSS.)
  4. Decision Trees Another language for representing and learning functions. The key concept supporting modularity is partitioning the input space.

Many other learning algorithms can be seen as falling into one of the above families.

In addition there are languages related to various aspects of learning.

  1. Reductions A language for translating between varying real-world losses and core learning algorithm optimizations.
  2. Feature Languages Exactly how features are specified varies from on learning algorithm to another. Several people have been working on languages for features that cope with sparsity or the cross-product nature of databases.
  3. Data interaction languages The statistical query model of learning algorithms provides a standardized interface between data and learning algorithm.

These lists surely miss some languages—feel free to point them out below.

With respect to research “interesting” language-related questions include:

  1. For what aspects of learning is a language missing? Anytime adhocery is encountered, this suggests that there is room for a language. Finding what is not there is both hard and valuable.
  2. Are any of these languages fundamentally flawed or fundamentally advantageous with respect to another language?
  3. What are the most easy to use and effective primitives for these languages?
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Lower Bounds for Learning Reductions

Learning reductions transform a solver of one type of learning problem into a solver of another type of learning problem. When we analyze these for robustness we can make statement of the form “Reduction R has the property that regret r (or loss) on subproblems of type A implies regret at most f ( r ) on the original problem of type B“.

A lower bound for a learning reduction would have the form “for all reductions R, there exists a learning problem of type B and learning algorithm for problems of type A where regret r on induced problems implies at least regret f ( r ) for B“.

The pursuit of lower bounds is often questionable because, unlike upper bounds, they do not yield practical algorithms. Nevertheless, they may be helpful as a tool for thinking about what is learnable and how learnable it is. This has already come up here and here.

At the moment, there is no coherent theory of lower bounds for learning reductions, and we have little understanding of how feasible they are or which techniques may be useful in proving them. Here is a rough summary of what I know:

  1. For structured prediction, we have a partially worked out lower bound for all reductions using the structure to only carry single bits. A proof for reductions using the structure in others ways seems tricky at the moment.
  2. For Reinforcement learning it may (this is unclear) be possible to prove a lower bound showing that prediction ability alone can not solve RL well.
  3. There are various results which can be thought of as lower bounds for more limited families of reductions. One example is analyzing exactly how badly margin optimization can underperform for 0-1 loss when there is noise.

Overall, this is a moderately interesting direction of research which has not been much investigated.

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Reopening RL->Classification

In research, it’s often the case that solving a problem helps you realize that it wasn’t the right problem to solve. This is the case for the “reduce RL to classification” problem with the solution hinted at here and turned into a paper here.

The essential difficulty is that the method of stating and analyzing reductions ends up being nonalgorithmic (unlike previous reductions) unless you work with learning from teleoperated robots as Greg Grudic does. The difficulty here is due to the reduction being dependent on the optimal policy (which a human teleoperator might simulate, but which is otherwise unavailable).

So, this problem is “open” again with the caveat that this time we want a more algorithmic solution.

Whether or not this is feasible at all is still unclear and evidence in either direction would greatly interest me. A positive answer might have many practical implications in the long run.

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Workshops are not Conferences

… and you should use that fact.

A workshop differs from a conference in that it is about a focused group of people worrying about a focused topic. It also differs in that a workshop is typically a “one-time affair” rather than a series. (The Snowbird learning workshop counts as a conference in this respect.)

A common failure mode of both organizers and speakers at a workshop is to treat it as a conference. This is “ok”, but it is not really taking advantage of the situation. Here are some things I’ve learned:

  1. For speakers: A smaller audience means it can be more interactive. Interactive means a better chance to avoid losing your audience and a more interesting presentation (because you can adapt to your audience). Greater focus amongst the participants means you can get to the heart of the matter more easily, and discuss tradeoffs more carefully. Unlike conferences, relevance is more valued than newness.
  2. For organizers: Not everything needs to be in a conference style presentation format (i.e. regularly spaced talks of 20-30 minute duration). Significant (and variable) question time, different talk durations, flexible rescheduling, and panel discussions can all work well.
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Question: “When is the right time to insert the loss function?”

Hal asks a very good question: “When is the right time to insert the loss function?” In particular, should it be used at testing time or at training time?

When the world imposes a loss on us, the standard Bayesian recipe is to predict the (conditional) probability of each possibility and then choose the possibility which minimizes the expected loss. In contrast, as the confusion over “loss = money lost” or “loss = the thing you optimize” might indicate, many people ignore the Bayesian approach and simply optimize their loss (or a close proxy for their loss) over the representation on the training set.

The best answer I can give is “it’s unclear, but I prefer optimizing the loss at training time”. My experience is that optimizing the loss in the most direct manner possible typically yields best performance. This question is related to a basic principle which both Yann LeCun(applied) and Vladimir Vapnik(theoretical) advocate: “solve the simplest prediction problem that solves the problem”. (One difficulty with this principle is that ‘simplest’ is difficult to define in a satisfying way.)

One reason why it’s unclear is that optimizing an arbitrary loss is not an easy thing for a learning algorithm to cope with. Learning reductions (which I am a big fan of) give a mechanism for doing this, but they are new and relatively untried.

Drew Bagnell adds: Another approach to integrating loss functions into learning is to try to re-derive ideas about probability theory appropriate for other loss functions. For instance, Peter Grunwald and A.P. Dawid present a variant on maximum entropy learning. Unfortunately, it’s even less clear how often these approaches lead to efficient algorithms.