Abstract
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.
Highlights
Hidden 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
Once a model is trained from the data, either using maximum likelihood (ML) or maximum a posteriori (MAP), the segmentation is given by the most likely state sequence obtained with the Viterbi algorithm [14]
ML or MAP point estimates of HMM parameters combined with the Viterbi-algorithm to compute a most likely sequence of hidden states and a segmentation of the input are most popular in practice
Summary
Hidden 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. Once a model is trained from the data, either using maximum likelihood (ML) or maximum a posteriori (MAP), the segmentation is given by the most likely state sequence obtained with the Viterbi algorithm [14]. As analytic integration of a complex high dimensional model is impossible for most distributions, the Bayesian approach requires the use of numerical integration techniques like MCMC [15], for example by direct Gibbs sampling [16] of model parameters and state paths. Maximal compression is to be expected for small number of discrete symbols and clearly compression ratio conflicts with fidelity in the analysis
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