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

• Main Authors: Shimazaki, Hideaki (Author), Amari, Shun-ichi (Author), Brown, Emery N. (Contributor), Grun, Sonja (Author)
• Other Authors: Harvard University- (Contributor), Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers, 2011-03-07T22:09:50Z.
• Subjects: Article
• Online Access: Get fulltext

 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.