A tutorial of techniques for improving standard Hidden Markov Model algorithms.

In this tutorial, we discuss two main algorithms for Hidden Markov Models or HMMs: the Viterbi algorithm and the expectation phase of the Baum-Welch algorithm, and we describe ways to improve their naïve implementations. For the Baum-Welch algorithm we first present an implementation of the expectation computations using constant space. We then discuss the classical implementation of this calculation and describe ways to reduce its space usage to logarithmic and O(square root n), with their respective CPU costs. We also note where each respective algorithm can be parallelized. For the Viterbi algorithm, we describe O(square root n) and logarithmic space algorithms which increase CPU use by a factor of two and by a logarithmic factor respectively. We also present two recent heuristics for decreasing space use, which in practice lead to logarithmic space use. Classical version of Viterbi cannot be parallelized by splitting sequence in several subsequences, but we show a parallelization that works if we are willing to pay a significant extra CPU cost. Finally we show a very simple parallelization trick which enables full usage of multiple CPUs/cores under the condition that they share memory.