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A Geometric Proof of Calibration

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 a 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 [Foster, D. 1999. A proof of calibration via Blackwell's approachability theorem. Games Econom. Behav. 29 73-78] in the case of binary outcomes) and highlights the intrinsic connection between approachability and calibration.
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Submitted on : Thursday, April 14, 2011 - 3:46:09 PM
Last modification on : Thursday, January 11, 2018 - 6:19:32 AM

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Gilles Stoltz, Shie Mannor. A Geometric Proof of Calibration. Mathematics of Operations Research, INFORMS, 2010, 35 (4), pp.721-727. ⟨10.1287/moor.1100.0465⟩. ⟨hal-00586044⟩

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