Analysis of higher-order neuronal interactions based on conditional inference

Higher-order neural interactions, i.e., interactions that cannot be reduced to interactions between pairs of cells, have received increasing attention in the context of recent attempts to understand the cooperative dynamics in cortical neural networks. Typically, likelihood-ratio tests of log-linear models are being employed for statistical inference. The parameter estimation of these models for simultaneously recorded single-neuron spiking activities is a crucial ingredient of this approach. Extending a previous investigation of a two-neuron system, we present here the general formulation of an exact test suited for the detection of positive higher-order interactions between m neurons. This procedure does not require the estimation of any interaction parameters and additionally optimizes the test power of the statistical inference. We apply the approach to a three-neuron system and show how second-order and third-order interactions can be reliably distinguished. We study the performance of the method as a function of the interaction strength.