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2014

A Bayesian Characterization of Relative Entropy

Baez, John C., Fritz, Tobias

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We give a new characterization of relative entropy, also known as the Kullback-Leibler divergence.

We use a number of interesting categories related to probability theory.
In particular, we consider a category FinStat where an object is a finite set equipped with a probability distribution, while a morphism is a measure-preserving function $f: X \to Y$ together with a stochastic right inverse $s: Y \to X$.
The function $f$ can be thought of as a measurement process, while s provides a hypothesis about the state of the measured system given the result of a measurement.

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J. Baez, T. Fritz and T. Leinster, A characterization of entropy in terms of information loss, Entropy
Original
1957
Earlier work this paper cites.
D. Petz, Characterization of the relative entropy of states of matrix algebras, Acta Math. Hungar
1992
Earlier work this paper cites.
D. Petz, Quantum entropy and its use
Original
1993
Earlier work this paper cites.

Similar

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M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities: Cauchy’s Equation and Jensen’s Inequality
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T. Fritz, Convex spaces I: definition and examples, available as arXiv:0903.5522
Original
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Then

T. Leinster, An operadic introduction to entropy, The n n -Category Café
2011
Later among the works it cites.
T. Leinster, The categorical origins of Lebesgue integration, talk at Category Theory 2014, 4 July 2014. Available at http://www.maths.ed.ac.uk/ ∼ \sim tl/cambridge_ct14/
2014
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