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The View From China

I’m visiting Beijing for the Pao-Lu Hsu Statistics Conference on Machine Learning.

I had several discussions about the state of Chinese research. Given the large population and economy, you might expect substantial research—more than has been observed at international conferences. The fundamental problem seems to be the Cultural Revolution which lobotimized higher education, and the research associated with it. There has been a process of slow recovery since then, which has begun to be felt in the research world via increased participation in international conferences and (now) conferences in China.

The amount of effort going into construction in Beijing is very impressive—people are literally building a skyscraper at night outside the window of the hotel I’m staying at (and this is not unusual). If a small fraction of this effort is later focused onto supporting research, the effect could be very substantial. General growth in China’s research portfolio should be expected.

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Idempotent-capable Predictors

One way to distinguish different learning algorithms is by their ability or inability to easily use an input variable as the predicted output. This is desirable for at least two reasons:

  1. Modularity If we want to build complex learning systems via reuse of a subsystem, it’s important to have compatible I/O.
  2. “Prior” knowledge Machine learning is often applied in situations where we do have some knowledge of what the right solution is, often in the form of an existing system. In such situations, it’s good to start with a learning algorithm that can be at least as good as any existing system.

When doing classification, most learning algorithms can do this. For example, a decision tree can split on a feature, and then classify. The real differences come up when we attempt regression. Many of the algorithms we know and commonly use are not idempotent predictors.

  1. Logistic regressors can not be idempotent, because all input features are mapped through a nonlinearity.
  2. Linear regressors can be idempotent—they just set the weight on one input feature to 1 and other features to 0.
  3. Regression trees are not idempotent, or (at least) not easily idempotent. In order to predict the same as an input feature, that input feature must be split many times.
  4. Bayesian approaches may or may not be easily idempotent, depending on the structure of the Bayesian Prior.

It isn’t clear how important the idempotent-capable property is. Successive approximation approaches such as boosting can approximate it in a fairly automatic maner. It may be of substantial importance for large modular systems where efficiency is important.

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Watchword: Online Learning

It turns out that many different people use the term “Online Learning”, and often they don’t have the same definition in mind. Here’s a list of the possibilities I know of.

  1. Online Information Setting Online learning refers to a problem in which unlabeled data comes, a prediction is made, and then feedback is acquired.
  2. Online Adversarial Setting Online learning refers to algorithms in the Online Information Setting which satisfy guarantees of the form: “For all possible sequences of observations, the algorithim has regret at most log ( number of strategies) with respect to the best strategy in a set.” This is sometimes called online learning with experts.
  3. Online Optimization Constraint Online learning refers to optimizing a predictor via a learning algorithm tunes parameters on a per-example basis. This may or may not be applied in the Online Information Setting, and the strategy may or may not satisfy Adversarial setting theory.
  4. Online Computational Constraint Online learning refers to an algorithmic constraint that the amount of computation per example is constant as the number of examples increases. Again, this doesn’t imply anything in particular about the Information setting in which it is applied.
  5. Lifelong Learning Online learning refers to learning in a setting where different tasks come at you over time, and you need to rapidly adapt to past mastered tasks.
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Interesting Papers at ICML 2007

Here are a few of the papers I enjoyed at ICML.

  1. Steffen Bickel, Michael Brüeckner, Tobias Scheffer, Discriminative Learning for Differing Training and Test Distributions There is a nice trick in this paper: they predict the probability that an unlabeled sample is in the training set vs. the test set, and then use this prediction to importance weight labeled samples in the training set. This paper uses a specific parametric model, but the approach is easily generalized.
  2. Steve Hanneke A Bound on the Label Complexity of Agnostic Active Learning This paper bounds the number of labels required by the A2 algorithm for active learning in the agnostic case. Last year we figured out agnostic active learning was possible. This year, it’s quantified. Hopefull soon, it will be practical.
  3. Sylvian Gelly, David Silver Combining Online and Offline Knowledge in UCT. This paper is about techniques for improving MoGo with various sorts of learning. MoGo has a fair claim at being the world’s best Go algorithm.

There were also a large number of online learning papers this year, especially if you count papers which use online learning techniques for optimization on batch datasets (as I do). This is expected, because larger datasets are becoming more common, and online learning makes more sense the larger the dataset. Many of these papers are of interest if your goal is learning fast while others are about extending online learning into new domains.

(Feel free to add any other papers of interest in the comments.)