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Parameterizing the approximate posterior of a generative model with neuralnetworks has become a common theme in recent machine learning research. Whileproviding appealing flexibility, this approach makes it difficult to impose orassess structural constraints such as conditional independence. We propose aframework for learning representations that relies on Auto-Encoding VariationalBayes and whose search space is constrained via kernel-based measures ofindependence. In particular, our method employs the $d$-variableHilbert-Schmidt Independence Criterion (dHSIC) to enforce independence betweenthe latent representations and arbitrary nuisance factors. We show how to applythis method to a range of problems, including the problems of learninginvariant representations and the learning of interpretable representations. Wealso present a full-fledged application to single-cell RNA sequencing(scRNA-seq). In this setting the biological signal is mixed in complex wayswith sequencing errors and sampling effects. We show that our methodout-performs the state-of-the-art in this domain.

Information Constraints on Auto-Encoding Variational Bayes