A broad range of cross-$m$-domain generation researches boil down to matching
a joint distribution by deep generative models (DGMs). Hitherto algorithms
excel in pairwise domains while as $m$ increases, remain struggling to scale
themselves to fit a joint distribution. In this paper, we propose a
domain-scalable DGM, i.e., MMI-ALI for $m$-domain joint distribution matching.
As an $m$-domain ensemble model of ALIs \cite{dumoulin2016adversarially},
MMI-ALI is adversarially trained with maximizing Multivariate Mutual
Information (MMI) w.r.t. joint variables of each pair of domains and their
shared feature. The negative MMIs are upper bounded by a series of feasible
losses that provably lead to matching $m$-domain joint distributions. MMI-ALI
linearly scales as $m$ increases and thus, strikes a right balance between
efficacy and scalability. We evaluate MMI-ALI in diverse challenging $m$-domain
scenarios and verify its superiority.

本文提出了一种适用于多域联合分布匹配的可扩展领域深度生成模型：MMI-ALI，它具有优秀的效能和可伸缩性，并且已经在多种具有挑战性的 $m$-domain 情景中得到了验证。

多元信息对抗集成用于可伸缩联合分布匹配

Multivariate-Information Adversarial Ensemble for Scalable Joint  Distribution Matching

A new generative adversarial network is developed for joint distribution
matching. Distinct from most existing approaches, that only learn conditional
distributions, the proposed model aims to learn a joint distribution of
multiple random variables (domains). This is achieved by learning to sample
from conditional distributions between the domains, while simultaneously
learning to sample from the marginals of each individual domain. The proposed
framework consists of multiple generators and a single softmax-based critic,
all jointly trained via adversarial learning. From a simple noise source, the
proposed framework allows synthesis of draws from the marginals, conditional
draws given observations from a subset of random variables, or complete draws
from the full joint distribution. Most examples considered are for joint
analysis of two domains, with examples for three domains also presented.

开发了一种新的生成对抗网络，用于联合分布匹配，并能够从多个随机变量中学习联合分布，同时学习采样每个单独领域的边缘分布和领域间的条件分布，该框架由多个生成器和一个基于 Softmax 的评论家组成，并通过对抗性学习进行联合训练。

JointGAN: 用生成式对抗网络实现多领域联合分布学习

JointGAN: Multi-Domain Joint Distribution Learning with Generative  Adversarial Nets

A Triangle Generative Adversarial Network ($\Delta$-GAN) is developed for
semi-supervised cross-domain joint distribution matching, where the training
data consists of samples from each domain, and supervision of domain
correspondence is provided by only a few paired samples. $\Delta$-GAN consists
of four neural networks, two generators and two discriminators. The generators
are designed to learn the two-way conditional distributions between the two
domains, while the discriminators implicitly define a ternary discriminative
function, which is trained to distinguish real data pairs and two kinds of fake
data pairs. The generators and discriminators are trained together using
adversarial learning. Under mild assumptions, in theory the joint distributions
characterized by the two generators concentrate to the data distribution. In
experiments, three different kinds of domain pairs are considered, image-label,
image-image and image-attribute pairs. Experiments on semi-supervised image
classification, image-to-image translation and attribute-based image generation
demonstrate the superiority of the proposed approach.

介绍了一种名为三角生成对抗网络 (Δ-GAN) 的模型，用于半监督跨域联合分布匹配，其中包括图像分类和图像转换等多领域应用。

三角形生成对抗网络

Triangle Generative Adversarial Networks

We investigate the non-identifiability issues associated with bidirectional
adversarial training for joint distribution matching. Within a framework of
conditional entropy, we propose both adversarial and non-adversarial approaches
to learn desirable matched joint distributions for unsupervised and supervised
tasks. We unify a broad family of adversarial models as joint distribution
matching problems. Our approach stabilizes learning of unsupervised
bidirectional adversarial learning methods. Further, we introduce an extension
for semi-supervised learning tasks. Theoretical results are validated in
synthetic data and real-world applications.

本研究旨在探究双向对抗训练中的不可识别性问题，并提出了基于条件熵的对抗和非对抗方法，用于无监督和监督任务的匹配联合分布学习。同时，将广泛的对抗模型统一为联合分布匹配问题，并提供了对于半监督学习任务的扩展方法。通过对合成数据和现实世界应用的验证，证明了理论结果的正确性。