DETECTING HIGHER-ORDER INTERACTIONS AMONG THE SPIKING EVENTS IN A GROUP OF NEURONS

We propose a formal framework for the description of interactions amon g groups of neurons. This framework is not restricted to the common ca se of pair interactions, but also incorporates higher-order interactio ns, which cannot be reduced to lower-order ones. We derive quantitativ e measures to detect the presence of such interactions in experimental data, by statistical analysis of the frequency distribution of higher -order correlations in multiple neuron spike train data. Our first ste p is to represent a frequency distribution as a Markov field on the mi nimal graph it induces. We then show the invariance of this graph with regard to changes of state. Clearly, only linear Markov fields can be adequately represented by graphs. Higher-order interdependencies, whi ch are reflected by the energy expansion of the distribution, require more complex graphical schemes, like constellations or assembly diagra ms, which we introduce and discuss. The coefficients of the energy exp ansion not only point to the interactions among neurons but are also a measure of their strength. We investigate the statistical meaning of detected interactions in an information theoretic sense and propose mi nimum relative entropy approximations as null hypotheses for significa nce tests. We demonstrate the various steps of our method in the situa tion of an empirical frequency distribution on six neurons, extracted from data on simultaneous multineuron recordings from the frontal cort ex of a behaving monkey and close with a brief outlook on future work.