State-space analysis on time-varying correlations in parallel spike sequences

  • Authors:

  • Hideaki Shimazaki;Shun-ichi Amari;Emery N. Brown;Sonja Grun

  • Affiliations:

  • Theoretical Neuroscience Group, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan;Theoretical Neuroscience Group, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan;Anesthesia and Critical Care, Massachusetts General Hospital, Boston, MA, USA;Theoretical Neuroscience Group, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan

  • Venue:
  • ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
  • Year:
  • 2009

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Abstract

A state-space method for simultaneously estimating time-dependent rate and higher-order correlation underlying parallel spike sequences is proposed. Discretized parallel spike sequences are modeled by a conditionally independent multivariate Bernoulli process using a log-linear link function, which contains a state of higher-order interaction factors. A nonlinear recursive filtering formula is derived from a log-quadratic approximation to the posterior distribution of the state. Together with a fixed-interval smoothing algorithm, time-dependent log-linear parameters are estimated. The smoothed estimates are optimized via EM-algorithm such that their prior covariance matrix maximizes the expected complete data log-likelihood. In addition, we perform model selection on the hierarchical log-linear state-space models to avoid over-fitting. Application of the method to simultaneously recorded neuronal spike sequences is expected to contribute to uncover dynamic cooperative activities of neurons in relation to behavior.