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Efficient feature selection from high-dimensional datasets is a veryimportant challenge in many data-driven fields of science and engineering. Weintroduce a statistical mechanics inspired strategy that addresses the problemof sparse feature selection in the context of binary classification byleveraging a computational scheme known as expectation propagation (EP). Thealgorithm is used in order to train a continuous-weights perceptron learning aclassification rule from a set of (possibly partly mislabeled) examplesprovided by a teacher perceptron with diluted continuous weights. We test themethod in the Bayes optimal setting under a variety of conditions and compareit to other state-of-the-art algorithms based on message passing and onexpectation maximization approximate inference schemes. Overall, oursimulations show that EP is a robust and competitive algorithm in terms ofvariable selection properties, estimation accuracy and computationalcomplexity, especially when the student perceptron is trained from correlatedpatterns that prevent other iterative methods from converging. Furthermore, ournumerical tests demonstrate that the algorithm is capable of learning onlinethe unknown values of prior parameters, such as the dilution level of theweights of the teacher perceptron and the fraction of mislabeled examples,quite accurately. This is achieved by means of a simple maximum likelihoodstrategy that consists in minimizing the free energy associated with the EPalgorithm.

Expectation propagation on the diluted Bayesian classifier