Sequential probability assignment via online convex programming using exponential families

Maxim Raginsky, Roummel F. Marcia, Jorge G. Silva, Rebecca M. Willett

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.