Variational Inference for Monte Carlo Objectives
Andriy Mnih Danilo J. Rezende Google DeepMind
Abstract
Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood, using samples from the variational posterior to compute the required gradients. Recently, Burda et al. (2016) have derived a tighter lower bound using a multi-sample importance sampling estimate of the likelihood and showed that optimizing it yields models that use more of their capacity and achieve higher likelihoods. This development showed the importance of such multi-sample objectives and explained the success of several related approaches.
中文速览
深度生成模型（deep generative model）的训练通常依赖变分推断，而当模型包含离散隐变量时，如何用多个重要性采样样本构成更紧的对数似然下界（multi-sample Monte Carlo objective）并高效估计其梯度，始终是一个棘手难题——现有方法要么有偏、要么方差极高。本文针对这一问题，提出了首个专为多样本重要性采样目标设计的无偏梯度估计器（unbiased gradient estimator），核心思路是用每个样本各自的低方差"学习信号"替换原本统一的高方差学习信号，从而在不引入额外可学习参数的前提下大幅降低方差。实验表明，该估计器在训练生成模型和结构化输出预测模型上，比经典的 NVIL 单样本估计器更简洁、更有效，且与现有有偏估计器性能相当甚至更优。这项工作填补了离散隐变量模型与多样本训练目标之间的方法论空白，为将离散潜变量模块集成进端到端可训练系统铺平了道路。
原文 arXiv:1602.06725;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1602.06725v2