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# Minimal Achievable Sufficient Statistic Learning

*Proceedings of the 36th International Conference on Machine Learning*, PMLR 97:1465-1474, 2019.

#### Abstract

We introduce Minimal Achievable Sufficient Statistic (MASS) Learning, a machine learning training objective for which the minima are minimal sufficient statistics with respect to a class of functions being optimized over (e.g., deep networks). In deriving MASS Learning, we also introduce Conserved Differential Information (CDI), an information-theoretic quantity that {—} unlike standard mutual information {—} can be usefully applied to deterministically-dependent continuous random variables like the input and output of a deep network. In a series of experiments, we show that deep networks trained with MASS Learning achieve competitive performance on supervised learning, regularization, and uncertainty quantification benchmarks.