De-randomizing MCMC dynamics with the diffusion Stein operator

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Conference article in proceedings
Date
2021
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Mcode
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Language
en
Pages
11
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Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021), Advances in Neural Information Processing Systems
Abstract
Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples from a diffusion process because the time evolution of its marginal distributions constitutes a curve that minimizes the KL-divergence via steepest descent in the Wasserstein space. Parallel to LD, Stein variational gradient descent (SVGD) similarly minimizes the KL, albeit endowed with a novel Stein-Wasserstein distance, by deterministically transporting a set of particle samples, thus de-randomizes the stochastic diffusion process. We propose de-randomized kernel-based particle samplers to all diffusion-based samplers known as MCMC dynamics. Following previous work in interpreting MCMC dynamics, we equip the Stein-Wasserstein space with a fiber-Riemannian Poisson structure, with the capacity of characterizing a fiber-gradient Hamiltonian flow that simulates MCMC dynamics. Such dynamics discretizes into generalized SVGD (GSVGD), a Stein-type deterministic particle sampler, with particle updates coinciding with applying the diffusion Stein operator to a kernel function. We demonstrate empirically that GSVGD can de-randomize complex MCMC dynamics, which combine the advantages of auxiliary momentum variables and Riemannian structure, while maintaining the high sample quality from an interacting particle system.
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Shen, Z, Heinonen, M & Kaski, S 2021, De-randomizing MCMC dynamics with the diffusion Stein operator . in Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021 . Advances in Neural Information Processing Systems, vol. 21, Neural Information Processing Systems Foundation, pp. 17507-17517, Conference on Neural Information Processing Systems, Virtual, Online, 06/12/2021 . < https://proceedings.neurips.cc/paper/2021/hash/9271905e840548b8cada6d60c0cfd93b-Abstract.html >