An Efficient Self-Tuning Explicit and Adaptive HMM with Duration Algorithm

We describe an efficient, self-tuning, explicit and adaptive, hidden Markov model with Duration (the ESTEAHMMD algorithm). The standard hidden Markov model (HMM) constrains state occupancy durations to be geometrically distributed, while the standard hidden Markov model with duration (HMMD) addresses this limitation, but at significant computational expense. A standard HMM requires computation of order O(T N N), where T is the period of observations and N is the number of states. An explicit-duration HMM (HMMD) requires computation of order O(T N N + T N D 2), where D is the maximum interval between state transitions, while a hidden semi-Markov HMMD requires computation of order O(T N N + T N D). The latter improvement is still fundamentally limited if D N (where D > 500, typically), and imposes a maximum state interval constraint that may be too restrictive in some situations such as intron modeling in gene structure identification. The ESTEAHMMD algorithm proposed here relaxes the maximum state interval constraint and requires computation of order O(T N N + T N D *), where D * is the bin number in an adaptive representation of the distribution on the interval between state transitions, and is typically reducible to ∼ 50 for standard single-peak probability distributions. This provides a means to do forward-backward and Viterbi algorithm HMMD computations at an expense only marginally greater than the standard HMM for N < 50; and at negligible added expense when N > 50.