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Robustness to outliers is a central issue in real-world machine learningapplications. While replacing a model to a heavy-tailed one (e.g., fromGaussian to Student-t) is a standard approach for robustification, it can onlybe applied to simple models. In this paper, based on Zellner's optimization andvariational formulation of Bayesian inference, we propose an outlier-robustpseudo-Bayesian variational method by replacing the Kullback-Leibler divergenceused for data fitting to a robust divergence such as the beta- andgamma-divergences. An advantage of our approach is that superior but complexmodels such as deep networks can also be handled. We theoretically prove that,for deep networks with ReLU activation functions, the \emph{influence function}in our proposed method is bounded, while it is unbounded in the ordinaryvariational inference. This implies that our proposed method is robust to bothof input and output outliers, while the ordinary variational method is not. Weexperimentally demonstrate that our robust variational method outperformsordinary variational inference in regression and classification with deepnetworks.

Variational Inference based on Robust Divergences