On the Generative Utility of Cyclic Conditionals

TL;DR

This paper investigates modeling joint distributions using cyclic conditional models, establishing theoretical criteria for their compatibility and determinacy, and introduces CyGen, a novel framework that improves data fitting by leveraging only these two conditionals.

Contribution

It provides a comprehensive theory for the compatibility and determinacy of cyclic conditionals and proposes CyGen, a new generative framework that operates solely on these conditionals.

Findings

CyGen better fits data compared to traditional models.

Theoretical criteria for compatibility and determinacy are established.

Experimental results demonstrate improved feature representation.

Abstract

We study whether and how can we model a joint distribution $p(x,z)$ using two conditional models $p(x|z)$ and $q(z|x)$ that form a cycle. This is motivated by the observation that deep generative models, in addition to a likelihood model $p(x|z)$, often also use an inference model $q(z|x)$ for extracting representation, but they rely on a usually uninformative prior distribution $p(z)$ to define a joint distribution, which may render problems like posterior collapse and manifold mismatch. To explore the possibility to model a joint distribution using only $p(x|z)$ and $q(z|x)$, we study their compatibility and determinacy, corresponding to the existence and uniqueness of a joint distribution whose conditional distributions coincide with them. We develop a general theory for operable equivalence criteria for compatibility, and sufficient conditions for determinacy. Based on the theory, we propose a novel generative modeling framework CyGen that only uses the two cyclic conditional models. We develop methods to achieve compatibility and determinacy, and to use the conditional models to fit and generate data. With the prior constraint removed, CyGen better fits data and captures more representative features, supported by both synthetic and real-world experiments.