Florencia Leonardi — Page 2

arXiv2008

Exponential inequalities for empirical unbounded context trees

In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the context tree of a Variable Length Markov Chain. As a consequence of the exponential bounds we obtain a strong consistency result. We generalize in this way several previous results in the field.

math.ST↗

arXiv2008

Detecting phylogenetic relations out from sparse context trees

The goal of this paper is to study the similarity between sequences using a distance between the \emph{context} trees associated to the sequences. These trees are defined in the framework of \emph{Sparse Probabilistic Suffix Trees} (SPST), and can be estimated using the SPST algorithm. We implement the Phyl-SPST package to compute the distance between the sparse context trees estimated with the SPST algorithm. The distance takes into account the structure of the trees, and indirectly the transition probabilities. We apply this approach to reconstruct a phylogenetic tree of protein sequences in the globin family of vertebrates. We compare this tree with the one obtained using the well-known PAM distance.

stat.AP↗