Sequential probability assignment via online convex programming using exponential families

Authors:
Maxim Raginsky;Roummel F. Marcia;Jorge Silva;Rebecca M. Willett
Affiliations:
ECE Department, Duke University, Durham, NC;ECE Department, Duke University, Durham, NC;ECE Department, Duke University, Durham, NC;ECE Department, Duke University, Durham, NC
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Year:
2009

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Abstract

This paper considers the problem of sequential assignment of probabilities (likelihoods) to elements of an individual sequence using an exponential family of probability distributions. We draw upon recent work on online convex programming to devise an algorithm that does not require computing posterior distributions given all current observations, involves simple primal-dual parameter updates, and achieves minimax per-round regret against slowly varying product distributions with marginals drawn from the same exponential family. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality.