Uncertainty Autoencoders: Learning Compressed Representations via Variational Information Maximization

The goal of statistical compressive sensing is to efficiently acquire and reconstruct high-dimensional signals with much fewer measurements than the data dimensionality, given access to a finite set of training signals. Current approaches do not learn the acquisition and recovery procedures end-to-end and are typically hand-crafted for sparsity based priors. We propose Uncertainty Autoencoders, a framework that jointly learns the acquisition (i.e., encoding) and recovery (i.e., decoding) procedures while implicitly modeling domain structure. Our learning objective optimizes for a variational lower bound to the mutual information between the signal and the measurements. We show how our framework provides a unified treatment to several lines of research in dimensionality reduction, compressive sensing, and generative modeling. Empirically, we demonstrate improvements of 32% on average over competing approaches for statistical compressive sensing of high-dimensional datasets.