On the Difference between the Information Bottleneck and the Deep Information Bottleneck.

Combining the information bottleneck model with deep learning by replacing mutual information terms with deep neural nets has proven successful in areas ranging from generative modelling to interpreting deep neural networks. In this paper, we revisit the deep variational information bottleneck and the assumptions needed for its derivation. The two assumed properties of the data, X and Y, and their latent representation T, take the form of two Markov chains T - X - Y and X - T - Y . Requiring both to hold during the optimisation process can be limiting for the set of potential joint distributions P ( X , Y , T ) . We, therefore, show how to circumvent this limitation by optimising a lower bound for the mutual information between T and Y: I ( T ; Y ) , for which only the latter Markov chain has to be satisfied. The mutual information I ( T ; Y ) can be split into two non-negative parts. The first part is the lower bound for I ( T ; Y ) , which is optimised in deep variational information bottleneck (DVIB) and cognate models in practice. The second part consists of two terms that measure how much the former requirement T - X - Y is violated. Finally, we propose interpreting the family of information bottleneck models as directed graphical models, and show that in this framework, the original and deep information bottlenecks are special cases of a fundamental IB model.

Information Bottleneck for Estimating Treatment Effects with Systematically Missing Covariates.

Estimating the effects of an intervention from high-dimensional observational data is a challenging problem due to the existence of confounding. The task is often further complicated in healthcare applications where a set of observations may be entirely missing for certain patients at test time, thereby prohibiting accurate inference. In this paper, we address this issue using an approach based on the information bottleneck to reason about the effects of interventions. To this end, we first train an information bottleneck to perform a low-dimensional compression of covariates by explicitly considering the relevance of information for treatment effects. As a second step, we subsequently use the compressed covariates to perform a transfer of relevant information to cases where data are missing during testing. In doing so, we can reliably and accurately estimate treatment effects even in the absence of a full set of covariate information at test time. Our results on two causal inference benchmarks and a real application for treating sepsis show that our method achieves state-of-the-art performance, without compromising interpretability.