Clustering Time Series with Nonlinear Dynamics: A Bayesian Non-Parametric and Particle-Based Approach

Alexander Lin, Yingzhuo Zhang, Jeremy Heng, Stephen A. Allsop, Kay M. Tye, Pierre E. Jacob, Demba Ba
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2476-2484, 2019.

Abstract

We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulus or contingency. Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear state-space models, we derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling cluster assignments and sampling parameter values that form the basis of the clustering. The Metropolis step employs recent innovations in particle-based methods. We apply the framework to clustering time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-lin19b, title = {Clustering Time Series with Nonlinear Dynamics: A Bayesian Non-Parametric and Particle-Based Approach}, author = {Lin, Alexander and Zhang, Yingzhuo and Heng, Jeremy and Allsop, Stephen A. and Tye, Kay M. and Jacob, Pierre E. and Ba, Demba}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {2476--2484}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/lin19b/lin19b.pdf}, url = {https://proceedings.mlr.press/v89/lin19b.html}, abstract = {We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulus or contingency. Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear state-space models, we derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling cluster assignments and sampling parameter values that form the basis of the clustering. The Metropolis step employs recent innovations in particle-based methods. We apply the framework to clustering time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.} }
Endnote
%0 Conference Paper %T Clustering Time Series with Nonlinear Dynamics: A Bayesian Non-Parametric and Particle-Based Approach %A Alexander Lin %A Yingzhuo Zhang %A Jeremy Heng %A Stephen A. Allsop %A Kay M. Tye %A Pierre E. Jacob %A Demba Ba %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-lin19b %I PMLR %P 2476--2484 %U https://proceedings.mlr.press/v89/lin19b.html %V 89 %X We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulus or contingency. Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear state-space models, we derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling cluster assignments and sampling parameter values that form the basis of the clustering. The Metropolis step employs recent innovations in particle-based methods. We apply the framework to clustering time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.
APA
Lin, A., Zhang, Y., Heng, J., Allsop, S.A., Tye, K.M., Jacob, P.E. & Ba, D.. (2019). Clustering Time Series with Nonlinear Dynamics: A Bayesian Non-Parametric and Particle-Based Approach. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2476-2484 Available from https://proceedings.mlr.press/v89/lin19b.html.

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