We propose a simple tractable pair hidden Markov model for pairwise sequence alignment that accounts for the presence of short tandem repeats. Using the framework of gain functions, we design several optimization criteria for decoding this model and
describe the resulting decoding algorithms, ranging from the traditional Viterbi and posterior decoding to block-based decoding algorithms specialized for our model. We compare the accuracy of individual decoding algorithms on simulated data and find our approach superior to the classical three-state pair HMM in simulations.
Hidden Markov models (HMMs) and their variants were successfully used for several sequence annotation tasks. Traditionally, inference with HMMs is done using the Viterbi and posterior decoding algorithms. However, recently a variety of different opti
mization criteria and associated computational problems were proposed. In this paper, we consider three HMM decoding criteria and prove their NP hardness. These criteria consider the set of states used to generate a certain sequence, but abstract from the exact locations of regions emitted by individual states. We also illustrate experimentally that these criteria are useful for HIV recombination detection.
In the small phylogeny problem we, are given a phylogenetic tree and gene orders of the extant species and our goal is to reconstruct all of the ancestral genomes so that the number of evolutionary operations is minimized. Algorithms for reconstructi
ng evolutionary history from gene orders are usually based on repeatedly computing medians of genomes at neighbouring vertices of the tree. We propose a new, more general approach, based on an iterative local optimization procedure. In each step, we propose candidates for ancestral genomes and choose the best ones by dynamic programming. We have implemented our method and used it to reconstruct evolutionary history of 16 yeast mtDNAs and 13 Campanulaceae cpDNAs.
Hidden Markov models are traditionally decoded by the Viterbi algorithm which finds the highest probability state path in the model. In recent years, several limitations of the Viterbi decoding have been demonstrated, and new algorithms have been dev
eloped to address them citep{Kall2005,Brejova2007,Gross2007,Brown2010}. In this paper, we propose a new efficient highest expected reward decoding algorithm (HERD) that allows for uncertainty in boundaries of individual sequence features. We demonstrate usefulness of our approach on jumping HMMs for recombination detection in viral genomes.
In this paper, we introduce the on-line Viterbi algorithm for decoding hidden Markov models (HMMs) in much smaller than linear space. Our analysis on two-state HMMs suggests that the expected maximum memory used to decode sequence of length $n$ with
$m$-state HMM can be as low as $Theta(mlog n)$, without a significant slow-down compared to the classical Viterbi algorithm. Classical Viterbi algorithm requires $O(mn)$ space, which is impractical for analysis of long DNA sequences (such as complete human genome chromosomes) and for continuous data streams. We also experimentally demonstrate the performance of the on-line Viterbi algorithm on a simple HMM for gene finding on both simulated and real DNA sequences.
