The Blackwell Information Bottleneck

I will talk about a new bottleneck method for learning data representations based on channel deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The bound itself is bounded above by the variational information bottleneck objective, and the two methods coincide in the regime of single-shot Monte Carlo approximations. The notion of deficiency provides a principled way of approximating complicated channels by relatively simpler ones. Deficiencies have a rich heritage in the theory of comparison of statistical experiments and have an operational interpretation in terms of the optimal risk gap of decision problems. Experiments demonstrate that the deficiency bottleneck can provide advantages in terms of minimal sufficiency as measured by information bottleneck curves, while retaining a good test performance in a classification task. I will also talk about an unsupervised generalization and relation to variational autoencoders. Finally, I discuss the utility of our method in estimating a quantity called the unique information which quantifies a deviation from the Blackwell order.

(Joint work with Guido Montufar, Departments of Mathematics and Statistics, UCLA)