Recently, we can simultaneously record spike data from many neurons in the field of electrophysiology, and thus it is required to develop mathematical framework for extracting higher-order correlation of neural firings. The joint probability of neural spike can be represented using the log-linear model. From statistical-mechanical point of view, the log-linear model can be regarded as a multi-body interacted Ising spin model or the Boltzman machine with higher-order interactions. The estimation of higher-order correlation of neural firing corresponds to that of higher-order interations Ising spin system, and to the hyper-parameter estimation in the Bayesian inference. In this paper, we apply maximization of marginal likelihood (MML) method to this problem, and discuss the properties of MML analytically using statistical-mechanical method.
URL : http://ptp.ipap.jp/link?PTPS/157/300/
DOI : 10.1143/PTPS.157.300