Variational Inference based on Robust Divergences
This work addresses robustness to outliers in variational inference, which is a domain-specific problem for machine learning practitioners using Bayesian methods with complex models like deep networks, representing an incremental improvement by adapting existing robust divergences.
The paper tackles the problem of outlier sensitivity in variational inference by replacing the Kullback-Leibler divergence with robust divergences like beta- and gamma-divergences, enabling robust pseudo-Bayesian methods for complex models such as deep networks. The authors theoretically prove bounded influence functions for robustness and experimentally show improved performance over ordinary variational inference in regression and classification tasks.
Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner's optimization and variational formulation of Bayesian inference, we propose an outlier-robust pseudo-Bayesian variational method by replacing the Kullback-Leibler divergence used for data fitting to a robust divergence such as the beta- and gamma-divergences. An advantage of our approach is that superior but complex models 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 ordinary variational inference. This implies that our proposed method is robust to both of input and output outliers, while the ordinary variational method is not. We experimentally demonstrate that our robust variational method outperforms ordinary variational inference in regression and classification with deep networks.