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PROPER LOCAL SCORING RULES
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DOI：10.1214/12-AOS971.png)
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摘要
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We investigate proper scoring rules for continuous distributions on the real line. It is known that the log score is the only such rule that depends on the quoted density only through its value at the outcome that materializes. Here we allow further dependence on a finite number in of derivatives of the density at the outcome, and describe a large class of such m-local proper scoring rules: these exist for all even m but no odd m. We further show that for m >= 2 all such m-local rules can be computed without knowledge of the normalizing constant of the distribution.
Keyword:
Bregman score
concavity
divergence
entropy
Euler-Lagrange equation
homogeneity
integration by parts
local function
score matching
variational methods
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