Expectation Propagation for Bayesian Multi-task Feature Selection

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In this paper we propose a Bayesian model for multi-task feature selection. This model is based on a generalized spike and slab sparse prior distribution that enforces the selection of a common subset of features across several tasks. Since exact Bayesian inference in this model is intractable, approximate inference is performed through expectation propagation (EP). EP approximates the posterior distribution of the model using a parametric probability distribution. This posterior approximation is particularly useful to identify relevant features for prediction. We focus on problems for which the number of features d is significantly larger than the number of instances for each task. We propose an efficient parametrization of the EP algorithm that offers a computational complexity linear in d. Experiments on several multi-task datasets show that the proposed model outperforms baseline approaches for single-task learning or data pooling across all tasks, as well as two state-of-the-art multi-task learning approaches. Additional experiments confirm the stability of the proposed feature selection with respect to various sub-samplings of the training data.