Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

Yury Lifshits, Shay Mozes, Oren Weimann, Michal Ziv-Ukelson

Research output: Contribution to journalArticlepeer-review


We present a method to speed up the dynamic program algorithms used for solving the HMM decoding and training problems for discrete time-independent HMMs. We discuss the application of our method to Viterbi's decoding and training algorithms (IEEE Trans. Inform. Theory IT-13:260-269, 1967), as well as to the forward-backward and Baum-Welch (Inequalities 3:1-8, 1972) algorithms. Our approach is based on identifying repeated substrings in the observed input sequence. Initially, we show how to exploit repetitions of all sufficiently small substrings (this is similar to the Four Russians method). Then, we describe four algorithms based alternatively on run length encoding (RLE), Lempel-Ziv (LZ78) parsing, grammar-based compression (SLP), and byte pair encoding (BPE). Compared to Viterbi's algorithm, we achieve speedups of Θ(log∈n) using the Four Russians method, log r using RLE, k using LZ78, k using SLP, and Ω(r) using BPE, where k is the number of hidden states, n is the length of the observed sequence and r is its compression ratio (under each compression scheme). Our experimental results demonstrate that our new algorithms are indeed faster in practice. We also discuss a parallel implementation of our algorithms.

Original languageEnglish
Pages (from-to)379-399
Number of pages21
Issue number3
StatePublished - Jul 2009
Externally publishedYes

Bibliographical note

Funding Information:
Y. Lifshits’ research was supported by the Center for the Mathematics of Information and the Lee Center for Advanced Networking.


  • Compression
  • Dynamic programming
  • HMM
  • Viterbi

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics


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