Stochastic Gradient MCMC with Repulsive Forces
Victor Gallego Institute of Mathematical Sciences (ICMAT)、SAMSI, Duke University、David Rios Insua Institute of Mathematical Sciences (ICMAT)、SAMSI, Duke University
Abstract
We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCMC method. Instead of treating each parallel chain independently from others, our proposed algorithm implements a repulsive force between particles, avoiding collapse and facilitating a better exploration of the parameter space. We also show how the addition of this noise term is necessary to obtain a valid SG-MCMC sampler, a significant difference with SVGD. Experiments with both synthetic distributions and real datasets illustrate the benefits of the proposed scheme.
中文速览
贝叶斯推断中同时运行多条马尔可夫链时，各链往往相互独立、容易聚集在同一区域，导致对参数空间的探索效率低下。本文将两种主流算法——随机梯度马尔可夫链蒙特卡罗（SG-MCMC）和斯坦变分梯度下降（SVGD）——纳入统一框架，指出SVGD加上一个噪声项本质上等价于一种多链SG-MCMC方法，并据此提出了新算法SGLD+R：它在各粒子（并行链）之间引入基于核函数的排斥力，使粒子主动分散、更充分地覆盖后验分布，同时保留了SG-MCMC收敛到真实后验的理论保证。实验表明，与独立并行SGLD及SVGD相比，SGLD+R在合成分布和真实数据集上均展现出更好的采样效率和后验估计质量。这项工作为在大规模贝叶斯推断中设计兼顾效率与准确性的多链采样器提供了新思路，且该框架可自然扩展至哈密顿动力学等更复杂的采样变体。
原文 arXiv:1812.00071;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1812.00071v2