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Particle Smoothing Variational Objectives
A body of recent work has focused on constructing a variational family of
filtered distributions using Sequential Monte Carlo (SMC). Inspired by this
work, we introduce Particle Smoothing Variational Objectives (SVO), a novel
backward simulation technique and smoothed approximate posterior defined
through a subsampling process. SVO augments support of the proposal and boosts
particle diversity. Recent literature argues that increasing the number of
samples K to obtain tighter variational bounds may hurt the proposal learning,
due to a signal-to-noise ratio (SNR) of gradient estimators decreasing at the
rate . As a second contribution, we develop
theoretical and empirical analysis of the SNR in filtering SMC, which motivates
our choice of biased gradient estimators. We prove that introducing bias by
dropping Categorical terms from the gradient estimate or using Gumbel-Softmax
mitigates the adverse effect on the SNR. We apply SVO to three nonlinear latent
dynamics tasks and provide statistics to rigorously quantify the predictions of
filtered and smoothed objectives. SVO consistently outperforms filtered
objectives when given fewer Monte Carlo samples on three nonlinear systems of
increasing complexity.Comment: 13 pages, 5 figure