Understanding Variational Inference in Function-Space

By David R. Burt, Sebastian W. Ober, Adrià Garriga-Alonso, Mark van der Wilk. 2020

51 citations recorded by the source corpus.

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural networks, where we only need the former, and the latter is hard to represent. In this work, we highlight some advantages and limitations of employing the Kullback-Leibler divergence in this setting. For example, we show that minimizing the KL divergence between a wide class of parametric distributions and the posterior induced by a (non-degenerate) Gaussian process prior leads to an ill-defined objective function. Then, we propose (featurized) Bayesian linear regression as a benchmark for `function-space' inference methods that directly measures approximation quality. We apply this methodology to assess aspects of the objective function and inference scheme considered in Sun, Zhang, Shi, and Grosse (2018), emphasizing the quality of approximation to Bayesian inference as opposed to predictive performance.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistical and Nonlinear Physics

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Citations in the corpus

Continual Learning via Sequential Function-Space Variational Inference (2023, background): “Given a dataset D = ( X , y ) , a prior p ( f ) and a variational family Q f , function-space variational inference (Burt et al., 2021; Matthews et al., 2016; Rudner et al., 2021; Sun et al., 2019) consists of finding the variational distribution q ( f ) ∈ Q f that maximizes This variational…”