PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A geometric proof of calibration
Shie Mannor and Gilles Stoltz
HAL / open archives 2009.

Abstract

We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and convex target set. Our proof captures the essence of existing proofs based on approachability (e.g., the proof by Foster, 1999 in case of binary outcomes) and highlights the intrinsic connection between approachability and calibration.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:5722
Deposited By:Gilles Stoltz
Deposited On:08 March 2010