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

TL;DR

QATS is a fast, scalable decoding algorithm for Hidden Markov Models that significantly reduces computational complexity, especially beneficial for large-scale problems with few states.

Contribution

Introduces QATS, a divide-and-conquer decoding method with polylogarithmic complexity in sequence length and cubic in state space size, improving efficiency over traditional algorithms.

Findings

QATS offers substantial speedups over Viterbi and PMAP algorithms.

QATS maintains high accuracy in state sequence estimation.

The R-package QATS implements the proposed algorithm.

Abstract

Hidden Markov models (HMMs) are characterized by an unobservable Markov chain and an observable process -- a noisy version of the hidden chain. Decoding the original signal from the noisy observations is one of the main goals in nearly all HMM based data analyses. Existing decoding algorithms such as Viterbi and the pointwise maximum a posteriori (PMAP) algorithm have computational complexity at best linear in the length of the observed sequence, and sub-quadratic in the size of the state space of the hidden chain. We present Quick Adaptive Ternary Segmentation (QATS), a divide-and-conquer procedure with computational complexity polylogarithmic in the length of the sequence, and cubic in the size of the state space, hence particularly suited for large scale HMMs with relatively few states. It also suggests an effective way of data storage as specific cumulative sums. In essence, the estimated sequence of states sequentially maximizes local likelihood scores among all local paths with at most three segments, and is meanwhile admissible. The maximization is performed only approximately using an adaptive search procedure. Our simulations demonstrate the speedups offered by QATS in comparison to Viterbi and PMAP, along with a precision analysis. An implementation of QATS is in the R-package QATS on GitHub.