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December 2013 Penalized estimation in high-dimensional hidden Markov models with state-specific graphical models
Nicolas Städler, Sach Mukherjee
Ann. Appl. Stat. 7(4): 2157-2179 (December 2013). DOI: 10.1214/13-AOAS662

Abstract

We consider penalized estimation in hidden Markov models (HMMs) with multivariate Normal observations. In the moderate-to-large dimensional setting, estimation for HMMs remains challenging in practice, due to several concerns arising from the hidden nature of the states. We address these concerns by $\ell_{1}$-penalization of state-specific inverse covariance matrices. Penalized estimation leads to sparse inverse covariance matrices which can be interpreted as state-specific conditional independence graphs. Penalization is nontrivial in this latent variable setting; we propose a penalty that automatically adapts to the number of states $K$ and the state-specific sample sizes and can cope with scaling issues arising from the unknown states. The methodology is adaptive and very general, applying in particular to both low- and high-dimensional settings without requiring hand tuning. Furthermore, our approach facilitates exploration of the number of states $K$ by coupling estimation for successive candidate values $K$. Empirical results on simulated examples demonstrate the effectiveness of the proposed approach. In a challenging real data example from genome biology, we demonstrate the ability of our approach to yield gains in predictive power and to deliver richer estimates than existing methods.

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Nicolas Städler. Sach Mukherjee. "Penalized estimation in high-dimensional hidden Markov models with state-specific graphical models." Ann. Appl. Stat. 7 (4) 2157 - 2179, December 2013. https://doi.org/10.1214/13-AOAS662

Information

Published: December 2013
First available in Project Euclid: 23 December 2013

zbMATH: 1283.62174
MathSciNet: MR3161717
Digital Object Identifier: 10.1214/13-AOAS662

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.7 • No. 4 • December 2013
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