Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling
Will Grathwohl Kuan-Chieh Wang Jörn-Henrik Jacobsen David Duvenaud Richard Zemel
Abstract
We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density $p(x)$ and the model density $q(x)$ defined by a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize the discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing $q(x)$ to minimize this discrepancy produces a novel method for training unnormalized models which scales more gracefully than existing methods. The ability to both learn and compare models is a unique feature of the proposed method.
中文速览
用神经网络来度量两个概率分布之间的"距离"，这件事可以绕过让人头疼的归一化常数问题——能量模型（Energy-Based Models, EBMs）的训练和评估长期被这个问题所困扰。作者提出了一种叫做"学习斯坦差异"（Learned Stein Discrepancy, LSD）的方法：用神经网络充当"批评者"，只需要访问模型对数密度的梯度，就能估计数据分布与模型分布之间的斯坦差异（Stein Discrepancy），而完全不依赖归一化常数或代价高昂的MCMC采样。在此基础上，他们既将LSD用于拟合优度检验（goodness-of-fit test），在高维数据上的表现超越了核化斯坦差异（KSD）等已有方法，又将其用作训练EBM的目标函数，相比基于MCMC的近似最大似然方法在高维场景下扩展性更好。这项工作的重要意义在于，它首次将EBM的训练与评估统一在同一框架下，且两者都不再依赖采样，为在复杂高维数据上可靠地学习和比较能量模型提供了实用工具。
原文 arXiv:2002.05616;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2002.05616v4