Agnostic Classi cation of MarkovianSequencesRan
Classiication of nite sequences without explicit knowledge of their statistical nature is a fundamental problem with many important applications. We propose a new information theoretic approach to this problem which is based on the following ingredients: (i) sequences are similar when they are likely to be generated by the same source; (ii) cross entropies can be estimated via \universal compression"; (iii) Markovian sequences can be optimally merged. With these ingredients we can classify discrete sequences whenever they can be compressed. We introduce the method and illustrate its application for hierarchical clustering of languages and for estimating similarities of protein sequences.