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From PAC-Bayes Bounds to KL Regularization
Pascal Germain · Alexandre Lacasse · Francois Laviolette · Mario Marchand · Sara Shanian

Wed Dec 09 07:00 PM -- 11:59 PM (PST) @ None #None

We show that convex KL-regularized objective functions are obtained from a PAC-Bayes risk bound when using convex loss functions for the stochastic Gibbs classifier that upper-bound the standard zero-one loss used for the weighted majority vote. By restricting ourselves to a class of posteriors, that we call quasi uniform, we propose a simple coordinate descent learning algorithm to minimize the proposed KL-regularized cost function. We show that standard ellp-regularized objective functions currently used, such as ridge regression and ellp-regularized boosting, are obtained from a relaxation of the KL divergence between the quasi uniform posterior and the uniform prior. We present numerical experiments where the proposed learning algorithm generally outperforms ridge regression and AdaBoost.

Author Information

Pascal Germain (INRIA Paris)
Alexandre Lacasse (Universite Laval)
Francois Laviolette (Université Laval)
Mario Marchand (Université Laval)
Sara Shanian (Laval University)

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