Concentration and Confidence for Discrete Bayesian Sequence Predictors
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Publication:2859227
DOI10.1007/978-3-642-40935-6_23zbMATH Open1407.62079DBLPconf/alt/LattimoreHS13arXiv1307.0127OpenAlexW2097663096WikidataQ58012248 ScholiaQ58012248MaRDI QIDQ2859227
Marcus Hutter, Tor Lattimore, Peter Sunehag
Publication date: 6 November 2013
Published in: Lecture Notes in Computer Science (Search for Journal in Brave)
Abstract: Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight high-probability bounds on the cumulative error, which is measured in terms of the Kullback-Leibler (KL) divergence. We also consider the problem of constructing upper confidence bounds on the KL and Hellinger errors similar to those constructed from Hoeffding-like bounds in the i.i.d. case. The new results are applied to show that Bayesian sequence prediction can be used in the Knows What It Knows (KWIK) framework with bounds that match the state-of-the-art.
Full work available at URL: https://arxiv.org/abs/1307.0127
Inference from stochastic processes and prediction (62M20) Bayesian inference (62F15) Learning and adaptive systems in artificial intelligence (68T05)
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