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Forward $\chi^2$ Divergence Based Variational Importance Sampling

Chengrui Li · Yule Wang · Weihan Li · Anqi Wu

Halle B #189
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Tue 7 May 7:30 a.m. PDT — 9:30 a.m. PDT

Abstract: Maximizing the marginal log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high marginal log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the marginal log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward $\chi^2$ divergence, to enhance marginal log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, in terms of both log-likelihood and model parameter estimation. Code: \url{}.

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