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A categorical characterization of relative entropy on standard Borel spaces (1703.08853v6)
Published 26 Mar 2017 in cs.IT and math.IT
Abstract: We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into Lawvere's category and we show convexity, lower semicontinuity and uniqueness.
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