Papers › Posterior Matching for Arbitrary Conditioning

Posterior Matching for Arbitrary Conditioning

28 Jan 2022arXiv:2201.12414archive 2025-07-28

Ryan R. Strauss, Junier B. Oliva

Arbitrary conditioning is an important problem in unsupervised learning, where we seek to model the conditional densities p(𝐱ᵤ |𝐱ₒ) that underly some data, for all possible non-intersecting subsets o, u ⊂{1, …, d}. However, the vast majority of density estimation only focuses on modeling the joint distribution p(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).

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