TY - GEN
T1 - Concentration and confidence for discrete Bayesian sequence predictors
AU - Lattimore, Tor
AU - Hutter, Marcus
AU - Sunehag, Peter
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Bayesian sequence prediction
KW - KWIK learning
KW - concentration of measure
KW - information theory
UR - http://www.scopus.com/inward/record.url?scp=84887453552&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-40935-6_23
DO - 10.1007/978-3-642-40935-6_23
M3 - Conference contribution
SN - 9783642409349
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 324
EP - 338
BT - Algorithmic Learning Theory - 24th International Conference, ALT 2013, Proceedings
T2 - 24th International Conference on Algorithmic Learning Theory, ALT 2013
Y2 - 6 October 2013 through 9 October 2013
ER -