We propose a  statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups that each comprise time series with similar dynamics . Our motivation comes from neuroscience  where an important problem is to identify, within a large assembly of neurons, sub-groups that respond similarly to a stimulus or contingency. In the neural setting, conditioned on cluster membership and the parameters governing the dynamics, time series within a cluster are assumed independent and generated according to a nonlinear binomial state-space model. We derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling of cluster membership and sampling of parameters of interest . The Metropolis step is a PMMH iteration that requires an unbiased, low variance estimate of the likelihood function of a nonlinear state-space model. We leverage recent results on controlled sequential Monte Carlo to estimate likelihood functions more efficiently compared to the bootstrap particle filter . We apply the framework to  time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.
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.
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general
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that each comprise time series with similar dynamics
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,
R
sub-groups
subsets
R
In the neural setting, conditioned on cluster membership and the parameters governing the dynamics, time series within a cluster are assumed independent and generated according to a nonlinear binomial
Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear
R
model. We
models, we
R
of cluster membership and sampling of parameters of interest
cluster assignments and sampling parameter values that form the basis of the clustering
R
is a PMMH iteration that requires an unbiased, low variance estimate of the likelihood function of a nonlinear state-space model. We leverage recent results on controlled sequential Monte Carlo to estimate likelihood functions more efficiently compared to the bootstrap particle filter
employs recent innovations in particle-based methods
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clustering