Sparsity-Inducing Categorical Prior Improves Robustness of the Information Bottleneck

The information bottleneck framework provides a systematic approach to learn representations that compress nuisance information in inputs and extract semantically meaningful information about the predictions. However, the choice of the prior distribution that fix the dimensionality across all the data can restrict the flexibility of this approach to learn robust representations. We present a novel sparsity-inducing spike-slab prior that uses sparsity as a mechanism to provide flexibility that allows each data point to learn its own dimension distribution. In addition, it provides a mechanism to learn a joint distribution of the latent variable and the sparsity. Thus, unlike other approaches, it can account for the full uncertainty in the latent space. Through a series of experiments using in-distribution and out-of-distribution learning scenarios on the MNIST and Fashion-MNIST data we show that the proposed approach improves the accuracy and robustness compared with the traditional fixed -imensional priors as well as other sparsity-induction mechanisms proposed in the literature.