Proper Scoring Rules and Bregman Divergence
نویسنده
چکیده
Proper scoring rules are a means of evaluating the quality of probabilistic forecasts. They induce dissimilarity measures of probability distributions known as Bregman divergences. We survey the literature on both entities and present their mathematical properties in a unified theoretical framework. This perspective allows us to identify score and Bregman divergences and characterize them together. We theorize the proper affine scoring rules and present a motivating example from robust estimation. And lastly, we develop the elements of the regularity theory of entropy functions and describe under what conditions a general convex function may be identified as the entropy function of a proper scoring rule and whether this association is unique.
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