Viterbi algorithm

About: Viterbi algorithm is a research topic. Over the lifetime, 7505 publications have been published within this topic receiving 154513 citations.

Factor graphs and the sum-product algorithm

Abstract: Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.

The viterbi algorithm

Abstract: The Viterbi algorithm (VA) is a recursive optimal solution to the problem of estimating the state sequence of a discrete-time finite-state Markov process observed in memoryless noise. Many problems in areas such as digital communications can be cast in this form. This paper gives a tutorial exposition of the algorithm and of how it is implemented and analyzed. Applications to date are reviewed. Increasing use of the algorithm in a widening variety of areas is foreseen.

Accelerated Profile HMM Searches

Abstract: Profile hidden Markov models (profile HMMs) and probabilistic inference methods have made important contributions to the theory of sequence database homology search. However, practical use of profile HMM methods has been hindered by the computational expense of existing software implementations. Here I describe an acceleration heuristic for profile HMMs, the "multiple segment Viterbi" (MSV) algorithm. The MSV algorithm computes an optimal sum of multiple ungapped local alignment segments using a striped vector-parallel approach previously described for fast Smith/Waterman alignment. MSV scores follow the same statistical distribution as gapped optimal local alignment scores, allowing rapid evaluation of significance of an MSV score and thus facilitating its use as a heuristic filter. I also describe a 20-fold acceleration of the standard profile HMM Forward/Backward algorithms using a method I call "sparse rescaling". These methods are assembled in a pipeline in which high-scoring MSV hits are passed on for reanalysis with the full HMM Forward/Backward algorithm. This accelerated pipeline is implemented in the freely available HMMER3 software package. Performance benchmarks show that the use of the heuristic MSV filter sacrifices negligible sensitivity compared to unaccelerated profile HMM searches. HMMER3 is substantially more sensitive and 100- to 1000-fold faster than HMMER2. HMMER3 is now about as fast as BLAST for protein searches.

A systematic comparison of various statistical alignment models

Abstract: We present and compare various methods for computing word alignments using statistical or heuristic models. We consider the five alignment models presented in Brown, Della Pietra, Della Pietra, and Mercer (1993), the hidden Markov alignment model, smoothing techniques, and refinements. These statistical models are compared with two heuristic models based on the Dice coefficient. We present different methods for combining word alignments to perform a symmetrization of directed statistical alignment models. As evaluation criterion, we use the quality of the resulting Viterbi alignment compared to a manually produced reference alignment. We evaluate the models on the German-English Verbmobil task and the French-English Hansards task. We perform a detailed analysis of various design decisions of our statistical alignment system and evaluate these on training corpora of various sizes. An important result is that refined alignment models with a first-order dependence and a fertility model yield significantly better results than simple heuristic models. In the Appendix, we present an efficient training algorithm for the alignment models presented.

Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference

Abstract: A maximum-likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite intersymbol interference and white Gaussian noise is developed, The structure comprises a sampled linear filter, called a whitened matched filter, and a recursive nonlinear processor, called the Viterbi algorithm. The outputs of the whitened matched filter, sampled once for each input symbol, are shown to form a set of sufficient statistics for estimation of the input sequence, a fact that makes obvious some earlier results on optimum linear processors. The Viterbi algorithm is easier to implement than earlier optimum nonlinear processors and its performance can be straightforwardly and accurately estimated. It is shown that performance (by whatever criterion) is effectively as good as could be attained by any receiver structure and in many cases is as good as if intersymbol interference were absent. Finally, a simplified but effectively optimum algorithm suitable for the most popular partial-response schemes is described.