Complexity-Based Approach to Calibration with Checking Rules

author: Alexander Rakhlin, Statistics Department, Wharton School, University of Pennsylvania
published: Aug. 2, 2011,   recorded: July 2011,   views: 3463


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We consider the problem of forecasting a sequence of outcomes from an unknown source. The quality of the forecaster is measured by a family of checking rules. We prove upper bounds on the value of the associated game, thus certifying the existence of a calibrated strategy for the forecaster. We show that complexity of the family of checking rules can be captured by the notion of a sequential cover introduced in [19]. Various natural assumptions on the class of checking rules are considered, including finiteness of Vapnik-Chervonenkis and Littlestone's dimensions.

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