Agnostic Bayesian Learning of Ensembles

Abstract

We propose a method for producing ensembles of predictors based on holdout estimations of their generalization performances. This approach uses a prior directly on the performance of predictors taken from a finite set of candidates and attempts to infer which one is best. Using Bayesian infer-ence, we can thus obtain a posterior that repre-sents our uncertainty about that choice and con-struct a weighted ensemble of predictors accord-ingly. This approach has the advantage of not re-quiring that the predictors be probabilistic them-selves, can deal with arbitrary measures of per-formance and does not assume that the data was actually generated from any of the predictors in the ensemble. Since the problem of finding the best (as opposed to the true) predictor among a class is known as agnostic PAC-learning, we re-fer to our method as agnostic Bayesian learning. We also propose a method to address the case where the performance estimate is obtained from k-fold cross validation. While being efficient and easily adjustable to any loss function, our exper-iments confirm that the agnostic Bayes approach is state of the art compared to common baselines such as model selection based on k-fold cross-validation or a learned linear combination of pre-dictor outputs.