Related papers: Discrete Langevin Sampler via Wasserstein Gradient Flow

Discrete Langevin Sampler via Wasserstein Gradient Flow

URL: http://arxiv.org/abs/2206.14897v1
Date: Wed, 29 Jun 2022 20:33:54 GMT
Title: Discrete Langevin Sampler via Wasserstein Gradient Flow
Authors: Haoran Sun, Hanjun Dai, Bo Dai, Haomin Zhou, Dale Schuurmans
Abstract summary: We show how LB functions give rise to LB dynamics corresponding to Wasserstein gradient flow in a discrete space. We propose a new algorithm, the Locally Balanced Jump (LBJ), by discretizing the LB dynamics with respect to simulation time.
Score: 102.94731267405056
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Recently, a family of locally balanced (LB) samplers has demonstrated excellent performance at sampling and learning energy-based models (EBMs) in discrete spaces. However, the theoretical understanding of this success is limited. In this work, we show how LB functions give rise to LB dynamics corresponding to Wasserstein gradient flow in a discrete space. From first principles, previous LB samplers can then be seen as discretizations of the LB dynamics with respect to Hamming distance. Based on this observation, we propose a new algorithm, the Locally Balanced Jump (LBJ), by discretizing the LB dynamics with respect to simulation time. As a result, LBJ has a location-dependent "velocity" that allows it to make proposals with larger distances. Additionally, LBJ decouples each dimension into independent sub-processes, enabling convenient parallel implementation. We demonstrate the advantages of LBJ for sampling and learning in various binary and categorical distributions.

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