The information loss of a stochastic map

James Fullwood; Arthur J. Parzygnat

doi:10.3390/e23081021

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arXiv · 2107.01975

The information loss of a stochastic map

James Fullwood·Arthur J. Parzygnat

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Abstract

We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic measure that we call conditional information loss. Although not functorial, these information measures are semi-functorial, a concept we introduce that is definable in any Markov category. We also introduce the notion of an entropic Bayes' rule for information measures, and we provide a characterization of conditional entropy in terms of this rule.

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James Fullwood, Arthur J. Parzygnat. 2021-07-05. The information loss of a stochastic map. https://doi.org/10.3390/e23081021

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