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

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.

[1]  M. Wilson,et al.  Analyzing Functional Connectivity Using a Network Likelihood Model of Ensemble Neural Spiking Activity , 2005, Neural Computation.

[2]  Piet de Jong,et al.  Covariances for smoothed estimates in state space models , 1988 .

[3]  Shun-ichi Amari,et al.  Methods of information geometry , 2000 .

[4]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[5]  Emery N. Brown,et al.  Estimating a State-space Model from Point Process Observations Emery N. Brown , 2022 .

[6]  Sonja Grün,et al.  Impact of Higher-Order Correlations on Coincidence Distributions of Massively Parallel Data , 2007, Summer School on Neural Networks.

[7]  Hirotugu Akaike,et al.  Likelihood and the Bayes procedure , 1980 .

[8]  Sonja Grün,et al.  Unitary Events in Multiple Single-Neuron Spiking Activity: II. Nonstationary Data , 2002, Neural Computation.

[9]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

[10]  Shun-ichi Amari,et al.  Information geometry on hierarchy of probability distributions , 2001, IEEE Trans. Inf. Theory.

[11]  F. Attneave,et al.  The Organization of Behavior: A Neuropsychological Theory , 1949 .

[12]  E N Brown,et al.  A Statistical Paradigm for Neural Spike Train Decoding Applied to Position Prediction from Ensemble Firing Patterns of Rat Hippocampal Place Cells , 1998, The Journal of Neuroscience.

[13]  Shun-ichi Amari,et al.  Information-Geometric Measure for Neural Spikes , 2002, Neural Computation.

[14]  J. Knott.  The organization of behavior: A neuropsychological theory , 1951 .

[15]  Uri T Eden,et al.  A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. , 2005, Journal of neurophysiology.

[16]  Günther Palm,et al.  Detecting higher-order interactions among the spiking events in a group of neurons , 1995, Biological Cybernetics.

[17]  A. Aertsen,et al.  Dynamics of neuronal interactions in monkey cortex in relation to behavioural events , 1995, Nature.