  In the contrastive analysis (CA) setting, machine learning practitioners are
specifically interested in discovering patterns that are enriched in a target
dataset as compared to a background dataset generated from sources of variation
irrelevant to the task at hand. For example, a biomedical data analyst may seek
to understand variations in genomic data only present among patients with a
given disease as opposed to those also present in healthy control subjects.
Such scenarios have motivated the development of contrastive latent variable
models to isolate variations unique to these target datasets from those shared
across the target and background datasets, with current state of the art models
based on the variational autoencoder (VAE) framework. However, previously
proposed models do not explicitly enforce the constraints on latent variables
underlying CA, potentially leading to the undesirable leakage of information
between the two sets of latent variables. Here we propose the moment matching
contrastive VAE (MM-cVAE), a reformulation of the VAE for CA that uses the
maximum mean discrepancy to explicitly enforce two crucial latent variable
constraints underlying CA. On three challenging CA tasks we find that our
method outperforms the previous state-of-the-art both qualitatively and on a
set of quantitative metrics.
