Sparsely correlated hidden Markov models with application to genome-wide location studies

Abstract

Multiply correlated datasets have become increasingly common in genome-wide location analysis of regulatory proteins and epigenetic modifications. Their correlation can be directly incorporated into a statistical model to capture underlying biological interactions, but such modeling quickly becomes computationally intractable. We present sparsely correlated hidden Markov models (scHMM), a novel method for performing simultaneous hidden Markov model (HMM) inference for multiple genomic datasets. In scHMM, a single HMM is assumed for each series, but the transition probability in each series depends on not only its own hidden states but also the hidden states of other related series. For each series, scHMM uses penalized regression to select a subset of the other data series and estimate their effects on the odds of each transition in the given series. Following this, hidden states are inferred using a standard forward-backward algorithm, with the transition probabilities adjusted by the model at each position, which helps retain the order of computation close to fitting independent HMMs (iHMM). Hence, scHMM is a collection of inter-dependent non-homogeneous HMMs, capable of giving a close approximation to a fully multivariate HMM fit. A simulation study shows that scHMM achieves comparable sensitivity to the multivariate HMM fit at a much lower computational cost. The method was demonstrated in the joint analysis of 39 histone modifications, CTCF and RNA polymerase II in human CD4+ T cells. scHMM reported fewer high-confidence regions than iHMM in this dataset, but scHMM could recover previously characterized histone modifications in relevant genomic regions better than iHMM. In addition, the resulting combinatorial patterns from scHMM could be better mapped to the 51 states reported by the multivariate HMM method of Ernst and Kellis. The scHMM package can be freely downloaded from http://sourceforge.net/p/schmm/ and is recommended for use in a linux environment.