Transfer Matrix Method for Instantaneous Spike Rate Estimation

Kazuho WATANABE  Hiroyuki TANAKA  Keiji MIURA  Masato OKADA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E92-D   No.7   pp.1362-1368
Publication Date: 2009/07/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E92.D.1362
Print ISSN: 0916-8532
Type of Manuscript: INVITED PAPER (Special Section on Large Scale Algorithms for Learning and Optimization)
Category: 
Keyword: 
spike rate estimation,  Bayesian estimation,  transfer matrix method,  smoothness prior,  

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Summary: 
The spike timings of neurons are irregular and are considered to be a one-dimensional point process. The Bayesian approach is generally used to estimate the time-dependent firing rate function from sequences of spike timings. It can also be used to estimate the firing rate from only a single sequence of spikes. However, the rate function has too many degrees of freedom in general, so approximation techniques are often used to carry out the Bayesian estimation. We applied the transfer matrix method, which efficiently computes the exact marginal distribution, to the estimation of the firing rate and developed an algorithm that enables the exact results to be obtained for the Bayesian framework. Using this estimation method, we investigated how the mismatch of the prior hyperparameter value affects the marginal distribution and the firing rate estimation.