2022/11/02 by Kaylee Yingxi Yang, Yang, Kaylee Yingxi, Andre Wibisono +1 · 1 citation
Computer Science · Biochemistry, Genetics and Molecular Biology · #Neural Networks and Applications #Bayesian Methods and Mixture Models #Gene Regulatory Network Analysis
paper · pdf · doi:10.48550/arxiv.2211.01512
Motivated by the increasingly popular Score-based Generative Modeling (SGM), we study the Inexact Langevin Dynamics (ILD) and Inexact Langevin Algorithm (ILA) where a score function estimate is used in place of the exact score. We establish \em stable biased convergence guarantees in terms of the Kullback-Leibler (KL) divergence. To achieve these guarantees, we impose two key assumptions: 1) the target distribution satisfies the log-Sobolev inequality, and 2) the error of score estimator exhibits a sub-Gaussian tail, referred to as Moment Generating Function (MGF) error assumption. Under the stronger L^∞ score error assumption, we obtain a stable convergence bound in Rényi divergence. We also generalize the proof technique to SGM, and derive a stable convergence bound in KL divergence. In addition, we explore the question of how to obtain a provably accurate score estimator. We demonstrate that a simple estimator based on kernel density estimation fulfills the MGF error assumption for sub-Gaussian target distributions, at the population level.