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- W2995615678 abstract "A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true underlying probability. We show that for binary classification, the divergence associated with smooth, proper, and convex loss functions is upper bounded by the Kullback-Leibler (KL) divergence, to within a normalization constant. This implies that by minimizing the logarithmic loss associated with the KL divergence, we minimize an upper bound to any choice of loss from this set. As such the logarithmic loss is universal in the sense of providing performance guarantees with respect to a broad class of accuracy measures. Importantly, this notion of universality is not problem-specific, enabling its use in diverse applications, including predictive modeling, data clustering and sample complexity analysis. Generalizations to arbitary finite alphabets are also developed. The derived inequalities extend several well-known $f$ -divergence results." @default.
- W2995615678 created "2019-12-26" @default.
- W2995615678 creator A5012874444 @default.
- W2995615678 creator A5066172831 @default.
- W2995615678 date "2020-03-01" @default.
- W2995615678 modified "2023-09-27" @default.
- W2995615678 title "Bregman Divergence Bounds and Universality Properties of the Logarithmic Loss" @default.
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- W2995615678 doi "https://doi.org/10.1109/tit.2019.2958705" @default.
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