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Calibration is about how correct your predictions are, on average. As an example, say you want to predict whether tomorrow is going to rain or not. If your perfectly calibrated model tells you it is going to rain with 70% chance, it means that, every time you get such a score from your estimator, 70% of the times it will actually rain. For the particular ...


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For discrete random variables $P$ and $Q$, the KL-divergence is defined as $$ D_{KL}(P || Q) = \sum_x P(x) \ln\frac{P(x)}{Q(x)} $$ So, as $Q \rightarrow P$, the ratio $P(x)/Q(x)$ approaches $1$ for all $x$ and the logarithm $\ln P(x)/Q(x)$ approaches zero. As probabilities are bounded to the range $[0, 1]$, each term in the sum, $P(x) \ln\frac{P(x)}{Q(x)}$ ...


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