Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers

• URL: http://arxiv.org/abs/2304.14390v1
• Date: Thu, 27 Apr 2023 17:54:57 GMT
• Title: Resampling Gradients Vanish in Differentiable Sequential Monte Carlo Samplers
• Authors: Johannes Zenn and Robert Bamler
• Abstract summary: 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) enables efficient optimization of the transition kernels of AIS and of the distributions. We propose to extend DAIS by a resampling step inspired by Sequential Monte Carlo.
• Score: 8.122270502556374
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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