Gradient Estimators for Implicit Models
Yingzhen Li、Richard E. Turner University of Cambridge Cambridge, CB2 1PZ, UK
Abstract
Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press approximate inference techniques relying on implicit distributions. The majority of existing approaches to learning implicit models rely on approximating the intractable distribution or optimisation objective for gradient-based optimisation, which is liable to produce inaccurate updates and thus poor models. This paper alleviates the need for such approximations by proposing the Stein gradient estimator, which directly estimates the score function of the implicitly defined distribution. The efficacy of the proposed estimator is empirically demonstrated by examples that include gradient-free MCMC, meta-learning for approximate inference and entropy regularised GANs that provide improved sample diversity.
中文速览
当我们手头只有一个能"生成样本"却无法直接写出概率公式的隐式模型（implicit model）——比如科学仿真器、生成对抗网络（GAN）或隐式变分推断——想要训练它就必须估计对数概率的梯度（即得分函数，score function），而这恰恰是个棘手的难题。本文提出了一种叫做"Stein梯度估计器"（Stein gradient estimator）的新方法，核心思路是利用Stein恒等式反推出得分函数的估计值，既有参数形式也有非参数的核方法形式，从而绕开了以往依赖判别器或核密度估计等近似手段所带来的不稳定性和偏差。作者在三个场景上验证了它的有效性：无梯度蒙特卡洛采样（gradient-free MCMC）、贝叶斯神经网络的元学习近似推断，以及加入熵正则化的GAN训练以提升生成样本的多样性，结果均优于现有竞争方法。这一工作为训练各类隐式概率模型提供了更准确、更稳定的梯度估计工具，有望广泛应用于科学仿真、图像生成和贝叶斯深度学习等领域。
原文 arXiv:1705.07107;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1705.07107v5