ActInf MathStream 012.1 ~ ELBOing Stein: Variational Bayes with Stein Mixture Inference, Ola Rønning

Ola Rønning
ELBOing Stein: Variational Bayes with Stein Mixture Inference
https://arxiv.org/abs/2410.22948
Ola Rønning, Eric Nalisnick, Christophe Ley, Padhraic Smyth, Thomas Hamelryck

Stein variational gradient descent (SVGD) [Liu and Wang, 2016] performs approximate Bayesian inference by representing the posterior with a set of particles. However, SVGD suffers from variance collapse, i.e. poor predictions due to underestimating uncertainty [Ba et al., 2021], even for moderately-dimensional models such as small Bayesian neural networks (BNNs). To address this issue, we generalize SVGD by letting each particle parameterize a component distribution in a mixture model. Our method, Stein Mixture Inference (SMI), optimizes a lower bound to the evidence (ELBO) and introduces user-specified guides parameterized by particles. SMI extends the Nonlinear SVGD framework [Wang and Liu, 2019] to the case of variational Bayes. SMI effectively avoids variance collapse, judging by a previously described test developed for this purpose, and performs well on standard data sets. In addition, SMI requires considerably fewer particles than SVGD to accurately estimate uncertainty for small BNNs. The synergistic combination of NSVGD, ELBO optimization and user-specified guides establishes a promising approach towards variational Bayesian inference in the case of tall and wide data.

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