Variational Inference based on Robust Divergences

Abstract

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.

References in corpus (2)

• Dropout Inference in Bayesian Neural Networks with Alpha-divergences
• A Minimax Optimal Algorithm for Crowdsourcing

Cited by in corpus (14)

• Generalized Variational Inference: Three arguments for deriving new Posteriors
• MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy
• Decision-Making with Auto-Encoding Variational Bayes
• Robust 3D reconstruction of dynamic scenes from single-photon lidar using Beta-divergences
• Alpha-Beta Divergence For Variational Inference
• When OT meets MoM: Robust estimation of Wasserstein Distance
• Robust Variational Autoencoder
• Variational Predictive Information Bottleneck
• Robust Variational Autoencoder for Tabular Data with Beta Divergence
• Frequentist Consistency of Generalized Variational Inference
• Generalized Bayesian Filtering via Sequential Monte Carlo
• Direct loss minimization algorithms for sparse Gaussian processes
• On Robust Pseudo-Bayes Estimation for the Independent Non-homogeneous Set-up
• Robustness Against Outliers For Deep Neural Networks By Gradient Conjugate Priors