Posterior Matching for Arbitrary Conditioning
This addresses the limitation in density estimation where joint distributions obscure conditional dependencies, benefiting researchers and practitioners in unsupervised learning by providing a general solution without requiring specialized models.
The paper tackles the problem of arbitrary conditioning in unsupervised learning, where modeling conditional densities for all feature subsets is challenging, and proposes Posterior Matching, a framework enabling Variational Autoencoders (VAEs) to perform this task without modifications, achieving comparable or superior results to state-of-the-art methods across various tasks and VAE types.
Arbitrary conditioning is an important problem in unsupervised learning, where we seek to model the conditional densities $p(\mathbf{x}_u \mid \mathbf{x}_o)$ that underly some data, for all possible non-intersecting subsets $o, u \subset \{1, \dots , d\}$. However, the vast majority of density estimation only focuses on modeling the joint distribution $p(\mathbf{x})$, in which important conditional dependencies between features are opaque. We propose a simple and general framework, coined Posterior Matching, that enables Variational Autoencoders (VAEs) to perform arbitrary conditioning, without modification to the VAE itself. Posterior Matching applies to the numerous existing VAE-based approaches to joint density estimation, thereby circumventing the specialized models required by previous approaches to arbitrary conditioning. We find that Posterior Matching is comparable or superior to current state-of-the-art methods for a variety of tasks with an assortment of VAEs (e.g.~discrete, hierarchical, VaDE).