A Hidden Markov Model With Binned Duration Algorithm
Stephen N. Winters-Hilt, Zuliang Jiang · IEEE Transactions on Signal Processing · 2009
The hidden Markov model with duration (HMMD) is critically important when the distributions on state intervals deviate significantly from the geometric distribution, such as for multimodal distributions and heavy-tailed distributions. Heavy-tailed distributions, in particular, are widespread in describing phenomena across the sciences, where the log-normal, student's-T, and Pareto distributions are heavy-tailed distributions that are almost as common as the normal and geometric distributions in descriptions of physical phenomena or man-made phenomena. The standard hidden Markov model (HMM) constrains state occupancy durations to be geometrically distributed, while HMMD avoids this limitation, but at significant computational expense. We propose a new algorithm, hidden Markov model with binned duration, whose result shows no loss of accuracy compared to the HMMD decoding performance and a computational expense that only differs from the much simpler and faster HMM decoding by a constant factor.