Arbitrary Conditional Distributions with Energy

Modeling distributions of covariates, or density estimation, is a core challenge in unsupervised learning. However, the majority of work only considers the joint distribution, which has limited relevance to practical situations. A more general and useful problem is arbitrary conditional density estimation, which aims to model any possible conditional distribution over a set of covariates, reflecting the more realistic setting of inference based on prior knowledge. We propose a novel method, Arbitrary Conditioning with Energy (ACE), that can simultaneously estimate the distribution p(\mathbf{x}_u \mid \mathbf{x}_o) for all possible subsets of unobserved features \mathbf{x}_u and observed features \mathbf{x}_o . ACE is designed to avoid unnecessary bias and complexity --- we specify densities with a highly expressive energy function and reduce the problem to only learning one-dimensional conditionals (from which more complex distributions can be recovered during inference).