Sequential universal modeling for non-binary sequences with constrained distributions

Sequential probability assignment and universal compression go hand in hand. We propose sequential for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded within a limited interval. algorithms essential many applications that require fast accurate estimation of the maximizing sequence probability. These include learning, regression, channel decoding, prediction, compression. On other hand, constrained introduce interesting theoretical twists must overcome order present efficient algorithms. Here, we focus on memoryless sources, precise analysis maximal minimax average distributions. show our algorithm based modified Krichevsky-Trofimov (KT) estimator is asymptotically optimal up $O(1)$ both redundancies. This paper follows addresses challenge presented \cite{stw08} suggested results binary case lay foundation studying larger alphabets.