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Simonas Tutlys (Nov 13 2022 at 04:50):recently came up with a fuzzification of commutativity through conditional entropy,the equation with abuse of notation is h(h2*f|h1)=h(h1) in a colimit triangle with the morphism f between two objects,more concrete is h(h2|h1,x)=h(h1) where x is the domain of f.if this is seen as an optimization objective (morphisms being machine learning models) then we could be able to optimize limits in various ways.can't code right now but would like a sanity check.it's also pretty beautiful that if we replace the | with = we get a commutativity equation on the left hand side
Simonas Tutlys (Nov 13 2022 at 05:48):Concrete in the sense that f is a hidden morphism/relationship in the data that we don't know of and the goal is to still be able to take (co)limits.
Simonas Tutlys (Nov 18 2022 at 06:58):Are there any conditional entropy estimators available?I have an old implementation from one book but it's extremely slow. Or other substitutes like conditional variance (variance of Y given X) or something?