Abstract
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 language | English |
---|---|
Pages (from-to) | 379-399 |
Number of pages | 21 |
Journal | Algorithmica |
Volume | 54 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2009 |
Externally published | Yes |
Bibliographical note
Funding Information:Y. Lifshits’ research was supported by the Center for the Mathematics of Information and the Lee Center for Advanced Networking.
Keywords
- Compression
- Dynamic programming
- HMM
- Viterbi
ASJC Scopus subject areas
- General Computer Science
- Computer Science Applications
- Applied Mathematics