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

In a data set comprising hundreds to thousands of neuronal time series (Brown et al., 2004), the ability to automatically identify subgroups of time series that respond similarly to an exogenous stimulus or contingency can provide insights into how neural computation is implemented at the level of groups of neurons. We consider the problem of clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of subgroups. Existing model-based approaches for clustering multiple time series rely on a generative model of the time series that is a mixture of linear-Gaussian state-space models, and can be further classified according to whether the number of mixture components is assumed to be known a priori, and according to the choice of inference procedure (MCMC or variational Bayes) (Inoue et al., 2006; Chiappa and Barber, 2007; Nieto-Barajas et al., 2014; Middleton, 2014; Saad and Mansinghka, 2018). In all cases, the linear-Gaussian assumption is crucial: it enables exact evaluation of the likelihood using a Kalman filter and the ability to sample exactly from the state sequences underlying each of the time series. For nonlinear and/or non-Gaussian state-space models, this likelihood cannot be evaluated in closed form and exact sampling is not possible.