2013/06/29 by Tor Lattimore, Marcus Hutter, Lattimore, Tor +3
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1307.0127
17 pages
arxiv created 2013/06/29 · arxiv updated 2013/07/02
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.