Partial Rejection Control for Robust Variational Inference in Sequential Latent Variable Models

Rahul Sharma, Soumya Banerjee, Dootika Vats, Piyush Rai

Keywords: dice enterprise, partial rejection control, sequential Monte-Carlo, Bernoulli factory, variational Inference, Rejection Sampling

Abstract: Effective variational inference crucially depends on a flexible variational family of distributions. Recent work has explored sequential Monte-Carlo (SMC) methods to construct variational distributions, which can, in principle, approximate the target posterior arbitrarily well, which is especially appealing for models with inherent sequential structure. However, SMC, which represents the posterior using a weighted set of particles, often suffers from particle weight degeneracy, leading to a large variance of the resulting estimators. To address this issue, we present a novel approach that leverages the idea of \emph{partial} rejection control (PRC) for developing a robust variational inference (VI) framework. In addition to developing a superior VI bound, we propose a novel marginal likelihood estimator constructed via a dice-enterprise: a generalization of the Bernoulli factory to construct unbiased estimators for SMC-PRC. The resulting variational lower bound can be optimized efficiently with respect to the variational parameters and generalizes several existing approaches in the VI literature into a single framework. We show theoretical properties of the lower bound and report experiments on various sequential models, such as the Gaussian state-space model and variational RNN, on which our approach outperforms existing methods.

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One-sentence Summary: We present a new family of approximate distributions VSMC-PRC that combines sequential Monte-Carlo, variational inference, and rejection sampling in a synergistic manner.

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