The Generalized Reparameterization Gradient
Francisco J. R. Ruiz University of Cambridge Columbia University、Michalis K. Titsias Athens University of Economics and Business、David M. Blei Columbia University
Abstract
The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma without further approximations, and most practical applications of the reparameterization gradient fit Gaussian distributions. In this paper, we introduce the generalized reparameterization gradient, a method that extends the reparameterization gradient to a wider class of variational distributions. Generalized reparameterizations use invertible transformations of the latent variables which lead to transformed distributions that weakly depend on the variational parameters. This results in new Monte Carlo gradients that combine reparameterization gradients and score function gradients. We demonstrate our approach on variational inference for two complex probabilistic models. The generalized reparameterization is effective: even a single sample from the variational distribution is enough to obtain a low-variance gradient.
中文速览
变分推断（variational inference）中，为了高效估计梯度，重参数化技巧（reparameterization gradient）是目前最流行的方法，但它几乎只能用于高斯分布，对 gamma、beta 等常见分布束手无策。本文提出「广义重参数化梯度」（generalized reparameterization gradient，G-Rep），核心思路是对隐变量做一个可逆变换，把它"标准化"成一个对变分参数依赖很弱的新变量，再把标准重参数化梯度与一个小的"修正项"（本质是得分函数梯度）相加，从而同时适用于高斯、gamma、beta 等更广泛的分布族。在非共轭矩阵分解模型和深度指数族模型上的实验表明，G-Rep 只需从变分分布中抽取单个样本就能得到方差很低的梯度估计，收敛速度显著快于黑盒变分推断（BBVI），精度也优于将一切都压缩成高斯的 ADVI。这项工作让高质量的随机梯度变分推断真正走向更丰富的概率模型，填补了重参数化技巧在非高斯分布上的空白。
原文 arXiv:1610.02287;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1610.02287v3