MOTIVATION: This work is motivated by the problem of identifying homozygosity islands on the genome of individuals in a population. Our method directly tackles the issue of identification of the homozygosity islands at the population level, without the need of analysing single individuals and then combine the results, as is made nowadays in state-of-the-art approaches. RESULTS: We propose regularized offline change-point methods to detect changes in the parameters of a multidimensional distribution when we have several aligned, independent samples of fixed resolution. We present a penalized maximum likelihood approach that can be efficiently computed by a dynamic programming algorithm or approximated by a fast binary segmentation algorithm. Both estimators are shown to converge almost surely to the set of change-points without the need of specifying a priori the number of change-points. In simulation, we observed similar performances from the exact and greedy estimators. Moreover, we provide a new methodology for the selection of the regularization constant which has the advantage of being automatic, consistent, and less prone to subjective analysis. AVAILABILITY AND IMPLEMENTATION: The data used in the application are from the Human Genome Diversity Project (HGDP) and is publicly available. Algorithms were implemented using the R software R Core Team (R: A Language and Environment for Statistical Computing. Vienna (Austria): R Foundation for Statistical Computing, 2020.) in the R package blockcpd, found at https://github.com/Lucas-Prates/blockcpd.

In this article we introduce an estimator for the number of communities in the Stochastic Block Model (SBM), based on the maximization of a penalized version of the so-called Krichevsky-Trofimov mixture distribution. We prove its eventual almost sure convergence to the underlying number of communities, without assuming a known upper bound on that quantity. Our results apply to both the dense and the sparse regimes. To our knowledge this is the first consistency result for the estimation of the number of communities in the SBM in the unbounded case, that is when the number of communities is allowed to grow with the same size.

Abstract Motivation: A central problem in genomics is to determine the function of a protein using the information contained in its amino acid sequence. Variable length Markov chains (VLMC) are a promising class of models that can effectively classify proteins into families and they can be estimated in linear time and space. Results: We introduce a new algorithm, called Sparse Probabilistic Suffix Trees (SPST), that identifies equivalences between the contexts of a VLMC. We show that, in many cases, the identification of these equivalences can improve the classification rate of the classical Probabilistic Suffix Trees (PST) algorithm. We also show that better classification can be achieved by identifying representative fingerprints in the amino acid chains, and this variation in the SPST algorithm is called F-SPST. Availability: The SPST algorithm can be freely downloaded from the site Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.