Laplace's rule of succession in information geometry
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last edited by Geo-Sci-InfoAuthor(s): Yann Ollivier
DOI URL: http://dx.doi.org/10.1007/978-3-319-25040-3_34
Video: http://www.youtube.com/watch?v=hBzvSaA9yRU
Slides: Ollivier_Laplace rule succession.pdf
Presentation: https://www.see.asso.fr/node/14288
Creative Commons Attribution-ShareAlike 4.0 InternationalAbstract:
When observing data x1, . . . , x t modelled by a probabilistic distribution pθ(x), the maximum likelihood (ML) estimator θML = arg max θ Σti=1 ln pθ(x i ) cannot, in general, safely be used to predict xt + 1. For instance, for a Bernoulli process, if only “tails” have been observed so far, the probability of “heads” is estimated to 0. (Thus for the standard log-loss scoring rule, this results in infinite loss the first time “heads” appears.)
