Robust Inference with Variational Bayes

Giordano, Ryan; Broderick, Tamara; Jordan, Michael I.

doi:10.48550/arxiv.1512.02578

Cited by 1 publication

(1 citation statement)

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“…The above expression looks similar to the ones derived in Giordano et al [2015] and Koh and Liang [2017]. However, discussion in Giordano et al [2015] focused on prior perturbation and expression in Koh and Liang [2017] is applicable only to maximum likelihood estimation. To our knowledge, ours is the first work to derive IFs of variational inference for data contamination.…”

Section: Influence Function Analysis For Specific Modelssupporting

confidence: 69%

Variational Inference based on Robust Divergences

Futami,

Sato,

Sugiyama

2017

Preprint

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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 β-and γ-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 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.

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Section: Influence Function Analysis For Specific Modelssupporting

confidence: 69%