@inproceedings{bb1042dfdcea4f6fb481349ac635ace8,
title = "Concentration and confidence for discrete Bayesian sequence predictors",
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.",
keywords = "Bayesian sequence prediction, KWIK learning, concentration of measure, information theory",
author = "Tor Lattimore and Marcus Hutter and Peter Sunehag",
year = "2013",
doi = "10.1007/978-3-642-40935-6\_23",
language = "English",
isbn = "9783642409349",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "324--338",
booktitle = "Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings",
note = "24th International Conference on Algorithmic Learning Theory, ALT 2013 ; Conference date: 06-10-2013 Through 09-10-2013",
}