Uncertainty in Artificial Intelligence
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A Bayesian Nonparametric Model for Spectral Estimation of Metastable Systems
Hao Wu
The identification of eigenvalues and eigenfunc- tions from simulation or experimental data is a fundamental and important problem for anal- ysis of metastable systems, because the domi- nant spectral components usually contain a lot of essential information of the metastable dy- namics on slow timescales. It has been shown that the dynamics of a strongly metastable sys- tem can be equivalently described as a hidden Markov model (HMM) under some technical as- sumptions and the spectral estimation can be performed through HMM learning. However, the spectral estimation with unknown number of dominant spectra is still a challenge in the framework of traditional HMMs, and the infi- nite HMMs developed based on stick-breaking processes cannot satisfactorily solved this prob- lem either. In this paper, we analyze the diffi- culties of spectral estimation for infinite HMMs, and present a new nonparametric model called stick-breaking half-weighted model (SB-HWM) to address this problem. The SB-HWM defines a sparse prior of eigenvalues and can be applied to Bayesian inference of dominant eigenpairs of metastable systems in a nonparametric manner. We demonstrate by simulations the advantages of applying SB-HWM to spectral estimation.
Pages: 878-887
PS Link:
PDF Link: /papers/14/p878-wu.pdf
AUTHOR = "Hao Wu ",
TITLE = "A Bayesian Nonparametric Model for Spectral Estimation of Metastable Systems",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "878--887"

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