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Compute Brier score for a probabilistic prediction.
tfp.substrates.numpy.stats.brier_score( labels, logits, name=None )
The [Brier score] is a loss function for probabilistic predictions over a
number of discrete outcomes. For a probability vector
p and a realized
k the Brier score is
sum_i p[i]*p[i] - 2*p[k]. Smaller values are
better in terms of prediction quality. The Brier score can be negative.
Compared to the cross entropy (aka logarithmic scoring rule) the Brier score does not strongly penalize events which are deemed unlikely but do occur, see . The Brier score is a strictly proper scoring rule and therefore yields consistent probabilistic predictions.
: G.W. Brier. Verification of forecasts expressed in terms of probability. Monthley Weather Review, 1950. : Tilmann Gneiting, Adrian E. Raftery. Strictly Proper Scoring Rules, Prediction, and Estimation. Journal of the American Statistical Association, Vol. 102, 2007. https://www.stat.washington.edu/raftery/Research/PDF/Gneiting2007jasa.pdf
Tensor, (N1, ..., Nk), containint elementwise Brier scores;