Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers

Johannes Zenn; Robert Bamler

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arXiv · 2304.14390

Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers

Johannes Zenn·Robert Bamler

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Abstract

Annealed Importance Sampling (AIS) moves particles along a Markov chain from a tractable initial distribution to an intractable target distribution. The recently proposed Differentiable AIS (DAIS) (Geffner and Domke, 2021; Zhang et al., 2021) enables efficient optimization of the transition kernels of AIS and of the distributions. However, we observe a low effective sample size in DAIS, indicating degenerate distributions. We thus propose to extend DAIS by a resampling step inspired by Sequential Monte Carlo. Surprisingly, we find empirically-and can explain theoretically-that it is not necessary to differentiate through the resampling step which avoids gradient variance issues observed in similar approaches for Particle Filters (Maddison et al., 2017; Naesseth et al., 2018; Le et al., 2018).

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Johannes Zenn, Robert Bamler. 2023-04-27. Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers. https://arxiv.org/abs/2304.14390

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