A Bayesian Nonparametric Model for Spectral Estimation of Metastable Systems

Hao Wu Free University of Berlin
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:922-931, 2014.

Abstract

The identification of eigenvalues and eigenfunctions from simulation or experimental data is a fundamental and important problem for analysis of metastable systems, because the dominant spectral components usually contain a lot of essential information of the metastable dynamics on slow timescales. It has been shown that the dynamics of a strongly metastable system can be equivalently described as a hidden Markov model (HMM) under some technical assumptions 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 infinite HMMs developed based on stick-breaking processes cannot satisfactorily solved this problem either. In this paper, we analyze the difficulties 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-berlin14a, title = {A {B}ayesian Nonparametric Model for Spectral Estimation of Metastable Systems}, author = {Berlin, Hao Wu Free University of}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {922--931}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/berlin14a/berlin14a.pdf}, url = {https://proceedings.mlr.press/r12/berlin14a.html}, abstract = {The identification of eigenvalues and eigenfunctions from simulation or experimental data is a fundamental and important problem for analysis of metastable systems, because the dominant spectral components usually contain a lot of essential information of the metastable dynamics on slow timescales. It has been shown that the dynamics of a strongly metastable system can be equivalently described as a hidden Markov model (HMM) under some technical assumptions 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 infinite HMMs developed based on stick-breaking processes cannot satisfactorily solved this problem either. In this paper, we analyze the difficulties 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A Bayesian Nonparametric Model for Spectral Estimation of Metastable Systems %A Hao Wu Free University of Berlin %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-berlin14a %I PMLR %P 922--931 %U https://proceedings.mlr.press/r12/berlin14a.html %V R12 %X The identification of eigenvalues and eigenfunctions from simulation or experimental data is a fundamental and important problem for analysis of metastable systems, because the dominant spectral components usually contain a lot of essential information of the metastable dynamics on slow timescales. It has been shown that the dynamics of a strongly metastable system can be equivalently described as a hidden Markov model (HMM) under some technical assumptions 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 infinite HMMs developed based on stick-breaking processes cannot satisfactorily solved this problem either. In this paper, we analyze the difficulties 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. %Z Reissued by PMLR on 04 October 2026.
APA
Berlin, H.W.F.U.o.. (2014). A Bayesian Nonparametric Model for Spectral Estimation of Metastable Systems. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:922-931 Available from https://proceedings.mlr.press/r12/berlin14a.html. Reissued by PMLR on 04 October 2026.

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