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From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning.
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V.A. Voevodskii, Categorical probability, Steklov Mathematical Institute Seminar, Nov. 20, 2008. http://www.mathnet.ru/php/seminars.phtml?option_lang=eng&presentid=259
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Jared Culbertson and Kirk Sturtz, A Categorical Foundation for Bayesian Probability, Applied Categorical Structures, 2013. http://link.springer.com/article/10.1007/s10485-013-9324-9
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