Neuronal extraction of statistical patterns embedded in time series

Neuronal systems need to process temporal signals. Here, we hypothesize that temporal (co-)fluctuations – corresponding to high-order statistics beyond the average activity – are relevant for computation. The proposed biologically inspired feedforward neuronal model is able to extract information from up to the third order cumulant to perform time series classification. This model relies on a nonlinear gain function to combine the different statistical orders of the inputs, after a usual weighted summation. In addition to the afferent synaptic weights, the nonlinear gain function is optimized, which enables the combination of cumulants in a synergistic manner to maximize the classification accuracy. The approach is demonstrated both on synthetic and real world datasets of multivariate time series to test the classification performance and to interpret the tunable gain function. Moreover, we show that our biological scheme makes a better use of the number of trainable parameters as compared to a classical machine-learning scheme. Our findings emphasize the benefit of biological neuronal architectures, paired with dedicated learning algorithms, for the processing of information embedded in higher-order statistical cumulants of temporal (co-)fluctuations.