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Hidden Markov models (HMMs) are characterized by an unobservable (hidden)Markov chain and an observable process, which is a noisy version of the hiddenchain. Decoding the original signal (i.e., hidden chain) from the noisyobservations is one of the main goals in nearly all HMM based data analyses.Existing decoding algorithms such as the Viterbi algorithm have computationalcomplexity at best linear in the length of the observed sequence, andsub-quadratic in the size of the state space of the Markov chain. We presentQuick Adaptive Ternary Segmentation (QATS), a divide-and-conquer procedurewhich decodes the hidden sequence in polylogarithmic computational complexityin the length of the sequence, and cubic in the size of the state space, henceparticularly suited for large scale HMMs with relatively few states. Theprocedure also suggests an effective way of data storage as specific cumulativesums. In essence, the estimated sequence of states sequentially maximizes locallikelihood scores among all local paths with at most three segments. Themaximization is performed only approximately using an adaptive searchprocedure. The resulting sequence is admissible in the sense that alltransitions occur with positive probability. To complement formal resultsjustifying our approach, we present Monte-Carlo simulations which demonstratethe speedups provided by QATS in comparison to Viterbi, along with a precisionanalysis of the returned sequences. An implementation of QATS in C++ isprovided in the R-package QATS and is available from GitHub.

Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models