Graphical Generative Adversarial Networks

Chongxuan Li, Max Welling, Jun Zhu, Bo Zhang

Abstract

Graphical GAN, 建模图像的结构信息（最近的好几篇工作都是围绕这个问题）
两种训练方法：global algorithm treats all variables as a wholel, ocal algorithm discriminates the individual local factors defined by the generative model separately.
两个Graphical GAN的具体实现，Gaussian Mixture GAN, State Space GAN

Introduction

Graphical GAN用Bayes网络表示变量间结构信息，还用深度隐式似然函数建模复杂数据，如图

左边表示GMGAN，右边表示SSGAN。白色圈表示显变量（可观测），灰色圈表示隐变量，单圈表示确定变量，双圈表示随机变量。$\theta$表示全局参数。
implicit probabilistic models: deterministically transform Z to X and the likelihood can be intractable
prescribed probabilistic models: define the likelihood functions for X with an explicit specification
amortized inference: introduce a recognition model, which is a family of distributions of a simple form, to approximate the true posterior
mean-field assumption: all of the dependency structures among the latent variables are ignored and the approximate posterior could be factorized as

$$q_H(z|x)=\prod_{i=1}^{|z|} q(z_i|x)$$
inverse factorization: views the original graphical model as a forward factorization and samples the latent variables given the observations efficiently by inverting G step by step
$$q_H(z|x)=\prod_{i=1}^{|z|} q(z_i|\partial_G(z_i) \cap z_{>i})$$