Here are two papers that seem particularly interesting at this year’s COLT.

- Gilles Blanchard and FranÃƒÂ§ois Fleuret, Occam’s Hammer. When we are interested in very tight bounds on the true error rate of a classifier, it is tempting to use a PAC-Bayes bound which can (empirically) be quite tight. A disadvantage of the PAC-Bayes bound is that it applies to a classifier which is randomized over a set of base classifiers rather than a single classifier. This paper shows that a similar bound can be proved which holds for a single classifier drawn from the set. The ability to safely use a single classifier is very nice. This technique applies generically to any base bound, so it has other applications covered in the paper.
- Adam Tauman Kalai. Learning Nested Halfspaces and Uphill Decision Trees. Classification PAC-learning, where you prove that any problem amongst some set is polytime learnable with respect to any distribution over the input
*X*is extraordinarily challenging as judged by lack of progress over a long period of time. This paper is about regression PAC-learning, and the results appear much more encouraging than exist in classification PAC-learning. Under the assumption that:- The level sets of the correct regressed value are halfspaces.
- The level sets obey a Lipschitz condition.

this paper proves that a good regressor can be PAC-learned using a boosting algorithm. (The “uphill decision trees” part of the paper is about one special case where you don’t need the Lipschitz condition.)

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