Open Access
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


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.


Download Citation

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.


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

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

Keywords: chromatin modeling , genome biology , graphical lasso , greedy backward pruning , HMM , MMDL , Model selection , universal regularization

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 4 • December 2013
Back to Top