Conditional Inference in Pre-trained Variational Autoencoders via Cross-coding

Variational Autoencoders (VAEs) are a popular generative model, but one in which conditional inference can be challenging. If the decomposition into query and evidence variables is fixed, conditional VAEs provide an attractive solution. To support arbitrary queries, one is generally reduced to Markov Chain Monte Carlo sampling methods that can suffer from long mixing times. In this paper, we propose an idea we term cross-coding to approximate the distribution over the latent variables after conditioning on an evidence assignment to some subset of the variables. This allows generating query samples without retraining the full VAE. We experimentally evaluate three variations of cross-coding showing that (i) they can be quickly optimized for different decompositions of evidence and query and (ii) they quantitatively and qualitatively outperform Hamiltonian Monte Carlo.