A-NICE-MC: Adversarial Training for MCMC
Jiaming Song Stanford University、Shengjia Zhao Stanford University、Stefano Ermon Stanford University
Abstract
Existing Markov Chain Monte Carlo (MCMC) methods are either based on general-purpose and domain-agnostic schemes, which can lead to slow convergence, or problem-specific proposals hand-crafted by an expert. In this paper, we propose A-NICE-MC, a novel method to automatically design efficient Markov chain kernels tailored for a specific domain. First, we propose an efficient likelihood-free adversarial training method to train a Markov chain and mimic a given data distribution. Then, we leverage flexible volume preserving flows to obtain parametric kernels for MCMC. Using a bootstrap approach, we show how to train efficient Markov chains to sample from a prescribed posterior distribution by iteratively improving the quality of both the model and the samples. Empirical results demonstrate that A-NICE-MC combines the strong guarantees of MCMC with the expressiveness of deep neural networks, and is able to significantly outperform competing methods such as Hamiltonian Monte Carlo.
中文速览
用神经网络来自动设计蒙特卡洛采样器（MCMC kernel）是个难题，因为既要保证采样的理论正确性，又要让网络高效可训练。A-NICE-MC 的核心思路是：把马尔可夫链看成一种隐式生成模型，借鉴生成对抗网络（GAN）的对抗训练框架来衡量链的样本与目标分布之间的差距，从而绕开难以计算的似然函数；同时，利用保体积流（volume-preserving flow）来参数化转移核，使 Metropolis-Hastings 接受率可以被精确计算，从根本上保证采样收敛到正确的后验分布。在没有目标分布样本的实际贝叶斯推断场景中，方法采用"自举（bootstrap）"策略——用当前链生成的样本反过来改进提议分布，迭代提升采样质量，并通过降低自相关来提高有效样本量。实验表明，A-NICE-MC 在多个基准任务上显著优于汉密顿蒙特卡洛（HMC）等经典方法，意义在于它首次将深度神经网络的表达能力与 MCMC 的严格理论保证有机结合，为自动化、领域自适应的贝叶斯推断提供了一条可行路径。
原文 arXiv:1706.07561;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1706.07561v3