Inferring hidden Markov models from noisy time sequences: a method to alleviate degeneracy in molecular dynamics

TL;DR

This paper introduces a novel method for inferring hidden Markov models from noisy time series data without assuming a predefined model structure, effectively detecting degenerate states and applicable to various biological data types.

Contribution

It presents a model-free approach based on causal state models for inferring HMMs from noisy data, improving detection of degenerate states and applicability to continuous biological signals.

Findings

Successfully recovers models from simulated data under high noise

Detects degenerate states in noisy datasets

Accurately infers transition rates in experimental FRET data

Abstract

We present a new method for inferring hidden Markov models from noisy time sequences without the necessity of assuming a model architecture, thus allowing for the detection of degenerate states. This is based on the statistical prediction techniques developed by Crutchfield et al., and generates so called causal state models, equivalent to hidden Markov models. This method is applicable to any continuous data which clusters around discrete values and exhibits multiple transitions between these values such as tethered particle motion data or Fluorescence Resonance Energy Transfer (FRET) spectra. The algorithms developed have been shown to perform well on simulated data, demonstrating the ability to recover the model used to generate the data under high noise, sparse data conditions and the ability to infer the existence of degenerate states. They have also been applied to new experimental FRET data of Holliday Junction dynamics, extracting the expected two state model and providing values for the transition rates in good agreement with previous results and with results obtained using existing maximum likelihood based methods.