Optimal Segmentation Using Tree Models

Sequence data are abundant in application areas such as computational biology, environmental sciences, and telecommunication. Many real-life sequences have a strong segmental structure, with segments of different complexities. In this paper we study the description of sequence segments using variable length Markov chains (VLMCs), also known as tree models. We discover the segment boundaries of a sequence and at the same time we obtain a VLMC for each segment. Such a context tree contains the probability distribution vectors that capture the essential features of the corresponding segment. We use the Bayesian information criterion (BIC) and the Krichevsky-Trofimov probability (KT) to select the number of segments of a sequence. On DNA data the method selects segments that closely correspond to the annotated regions of the genes.