Machine Learning (Theory)


Netflix nearly done

A $1M qualifying result was achieved on the public Netflix test set by a 3-way ensemble team. This is just in time for Yehuda‘s presentation at KDD, which I’m sure will be one of the best attended ever.

This isn’t quite over—there are a few days for another super-conglomerate team to come together and there is some small chance that the performance is nonrepresentative of the final test set, but I expect not.

Regardless of the final outcome, the biggest lesson for ML from the Netflix contest has been the formidable performance edge of ensemble methods.


A NIPS paper

I’m skipping NIPS this year in favor of Ada, but I wanted to point out this paper by Andriy Mnih and Geoff Hinton. The basic claim of the paper is that by carefully but automatically constructing a binary tree over words, it’s possible to predict words well with huge computational resource savings over unstructured approaches.

I’m interested in this beyond the application to word prediction because it is relevant to the general normalization problem: If you want to predict the probability of one of a large number of events, often you must compute a predicted score for all the events and then normalize, a computationally inefficient operation. The problem comes up in many places using probabilistic models, but I’ve run into it with high-dimensional regression.

There are a couple workarounds for this computational bug:

  1. Approximate. There are many ways. Often the approximations are uncontrolled (i.e. can be arbitrarily bad), and hence finicky in application.
  2. Avoid. You don’t really want a probability, you want the most probable choice which can be found more directly. Energy based model update rules are an example of that approach and there are many other direct methods from supervised learning. This is great when it applies, but sometimes a probability is actually needed.

This paper points out that a third approach can be viable empirically: use a self-normalizing structure. It seems highly likely that this is true in other applications as well.


NIPS 2008 workshop on ‘Learning over Empirical Hypothesis Spaces’

This workshop asks for insights how far we may/can push the theoretical boundary of using data in the design of learning machines. Can we express our classification rule in terms of the sample, or do we have to stick to a core assumption of classical statistical learning theory, namely that the hypothesis space is to be defined independent from the sample? This workshop is particularly interested in – but not restricted to – the ‘luckiness framework’ and the recently introduced notion of ‘compatibility functions’ in a semi-supervised learning context (more information can be found at


Automated Labeling

One of the common trends in machine learning has been an emphasis on the use of unlabeled data. The argument goes something like “there aren’t many labeled web pages out there, but there are a huge number of web pages, so we must find a way to take advantage of them.” There are several standard approaches for doing this:

  1. Unsupervised Learning. You use only unlabeled data. In a typical application, you cluster the data and hope that the clusters somehow correspond to what you care about.
  2. Semisupervised Learning. You use both unlabeled and labeled data to build a predictor. The unlabeled data influences the learned predictor in some way.
  3. Active Learning. You have unlabeled data and access to a labeling oracle. You interactively choose which examples to label so as to optimize prediction accuracy.

It seems there is a fourth approach worth serious investigation—automated labeling. The approach goes as follows:

  1. Identify some subset of observed values to predict from the others.
  2. Build a predictor.
  3. Use the output of the predictor to define a new prediction problem.
  4. Repeat…

Examples of this sort seem to come up in robotics very naturally. An extreme version of this is:

  1. Predict nearby things given touch sensor output.
  2. Predict medium distance things given the nearby predictor.
  3. Predict far distance things given the medium distance predictor.

Some of the participants in the LAGR project are using this approach.

A less extreme version was the DARPA grand challenge winner where the output of a laser range finder was used to form a road-or-not predictor for a camera image.

These automated labeling techniques transform an unsupervised learning problem into a supervised learning problem, which has huge implications: we understand supervised learning much better and can bring to bear a host of techniques.

The set of work on automated labeling is sketchy—right now it is mostly just an observed-as-useful technique for which we have no general understanding. Some relevant bits of algorithm and theory are:

  1. Reinforcement learning to classification reductions which convert rewards into labels.
  2. Cotraining which considers a setting containing multiple data sources. When predictors using different data sources agree on unlabeled data, an inferred label is automatically created.

It’s easy to imagine that undiscovered algorithms and theory exist to guide and use this empirically useful technique.


The Everything Ensemble Edge

Tags: Bayesian,Empirical,Papers jl@ 7:38 am

Rich Caruana, Alexandru Niculescu, Geoff Crew, and Alex Ksikes have done a lot of empirical testing which shows that using all methods to make a prediction is more powerful than using any single method. This is in rough agreement with the Bayesian way of solving problems, but based upon a different (essentially empirical) motivation. A rough summary is:

  1. Take all of {decision trees, boosted decision trees, bagged decision trees, boosted decision stumps, K nearest neighbors, neural networks, SVM} with all reasonable parameter settings.
  2. Run the methods on each problem of 8 problems with a large test set, calibrating margins using either sigmoid fitting or isotonic regression.
  3. For each loss of {accuracy, area under the ROC curve, cross entropy, squared error, etc…} evaluate the average performance of the method.

A series of conclusions can be drawn from the observations.

  1. (Calibrated) boosted decision trees appear to perform best, in general although support vector machines and neural networks give credible near-best performance.
  2. The metalearning algorithm which simply chooses the best (based upon a small validation set) performs much better.
  3. A metalearning algorithm which combines the predictors in an ensemble using stepwise refinement of validation set performance appears to perform even better.

There are a number of caveats to this work: it was only applied on large datasets there is no guarantee that the datasets are representative of your problem (although efforts were made to be representative in general), and the size of the training set was fixed rather than using the natural size given by the problem. Despite all these caveats, the story told above seems compelling: if you want maximum performance, you must try many methods and somehow combine them.

The most significant drawback of this method is computational complexity. Techniques for reducing the computational complexity are therefore of significant interest. It seems plausible that there exists some learning algorithm which typically performs well whenever any of the above algorithms can perform well at a computational cost which is significantly less than “run all algorithm on all settings and test”.

A fundamental unanswered question here is “why?” in several forms. Why have the best efforts of many machine learning algorithm designers failed to capture all the potential predictive strength into a single coherent learning algorithm? Why do ensembles give such a significant consistent edge in practice? A great many papers follow the scheme: invent a new way to create ensembles, test, observe that it improves prediction performance at the cost of more computation, and publish. There are several pieces of theory explain individual ensemble methods, but we seem to have no convincing theoretical statement explaining why they almost always work.

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