BackgroundHidden Markov Models (HMM) are often used for analyzing Comparative Genomic Hybridization (CGH) data to identify chromosomal aberrations or copy number variations by segmenting observation sequences. For efficiency reasons the parameters of a HMM are often estimated with maximum likelihood and a segmentation is obtained with the Viterbi algorithm. This introduces considerable uncertainty in the segmentation, which can be avoided with Bayesian approaches integrating out parameters using Markov Chain Monte Carlo (MCMC) sampling. While the advantages of Bayesian approaches have been clearly demonstrated, the likelihood based approaches are still preferred in practice for their lower running times; datasets coming from high-density arrays and next generation sequencing amplify these problems.ResultsWe propose an approximate sampling technique, inspired by compression of discrete sequences in HMM computations and by kd-trees to leverage spatial relations between data points in typical data sets, to speed up the MCMC sampling.ConclusionsWe test our approximate sampling method on simulated and biological ArrayCGH datasets and high-density SNP arrays, and demonstrate a speed-up of 10 to 60 respectively 90 while achieving competitive results with the state-of-the art Bayesian approaches.Availability: An implementation of our method will be made available as part of the open source GHMM library from http://ghmm.org.

Bayesian computations with Hidden Markov Models (HMMs) are often avoided in practice. Instead, due to reduced running time, point estimates -maximum likelihood (ML) or maximum a posterior (MAP) -are obtained and observation sequences are segmented based on the Viterbi path, even though the lack of accuracy and dependency on starting points of the local optimization are well known. We propose a method to speed-up Bayesian computations which addresses this problem for regular and time-dependent HMMs with discrete observations. In particular, we show that by exploiting sequence repetitions, using the four Russians method, and the conditional dependency structure, it is possible to achieve a Θ(log T ) speed-up, where T is the length of the observation sequence. Our experimental results on identification of segments of homogeneous nucleic acid composition, known as the DNA segmentation problem, show that the speed-up is also observed in practice. Availability: An implementation of our method will be available as part of the open source GHMM library from http://ghmm.org.

Motivation: Mapping billions of reads from next generation sequencing experiments to reference genomes is a crucial task, which can require hundreds of hours of running time on a single CPU even for the fastest known implementations. Traditional approaches have difficulties dealing with matches of large edit distance, particularly in the presence of frequent or large insertions and deletions (indels). This is a serious obstacle both in determining the spectrum and abundance of genetic variations and in personal genomics.Results: For the first time, we adopt the approximate string matching paradigm of geometric embedding to read mapping, thus rephrasing it to nearest neighbor queries in a q-gram frequency vector space. Using the L1 distance between frequency vectors has the benefit of providing lower bounds for an edit distance with affine gap costs. Using a cache-oblivious kd-tree, we realize running times, which match the state-of-the-art. Additionally, running time and memory requirements are about constant for read lengths between 100 and 1000 bp. We provide a first proof-of-concept that geometric embedding is a promising paradigm for read mapping and that L1 distance might serve to detect structural variations. TreQ, our initial implementation of that concept, performs more accurate than many popular read mappers over a wide range of structural variants.Availability and implementation: TreQ will be released under the GNU Public License (GPL), and precomputed genome indices will be provided for download at http://treq.sf.net.Contact: pavelm@cs.rutgers.eduSupplementary information: Supplementary data are available at Bioinformatics online.

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