Spectral Learning of Binomial HMMs for DNA Methylation Data

TL;DR

This paper introduces a spectral learning algorithm for Binomial Hidden Markov Models tailored for DNA methylation data, offering a computationally efficient alternative to EM with theoretical guarantees and real data evaluation.

Contribution

The paper extends spectral methods to Binomial HMMs using a new feature-map approach, enabling efficient learning with theoretical performance guarantees.

Findings

Algorithm performs well on real DNA methylation data.

Provides theoretical guarantees for the spectral method.

Outperforms traditional EM in computational efficiency.

Abstract

We consider learning parameters of Binomial Hidden Markov Models, which may be used to model DNA methylation data. The standard algorithm for the problem is EM, which is computationally expensive for sequences of the scale of the mammalian genome. Recently developed spectral algorithms can learn parameters of latent variable models via tensor decomposition, and are highly efficient for large data. However, these methods have only been applied to categorial HMMs, and the main challenge is how to extend them to Binomial HMMs while still retaining computational efficiency. We address this challenge by introducing a new feature-map based approach that exploits specific properties of Binomial HMMs. We provide theoretical performance guarantees for our algorithm and evaluate it on real DNA methylation data.