Estimation of Functional Dependence in High-Dimensional Spike-Field Activity

Behavior is encoded across spatiotemoral scales of brain activity, from small-scale spikes to large-scale local field potentials (LFP). Identifying the functional dependence between spikes and LFP networks during behavior can help understand neural encoding and improve future neurotechnologies, but is difficult to achieve. First, spikes and LFP have different statistical characteristics (binary spikes vs. continuous LFPs) and time-scales. Second, given the prohibitively large number of spike channels and LFP features recorded in today's experiments, learning dependencies between all recorded signals is challenging and prone to overfitting. To solve this challenge, we present a model-based approach to estimate the functional dependence between high-dimensional field features and neuronal spikes. We model the binary time-series of spikes for each neuron as a point process dependent on the behavioral states and LFP features across the network. Given the prohibitively large number of possible spike-LFP dependency parameters, we first employ an Ll-regularization technique to learn the point process model during both supervised and unsupervised learning to ease detection of significant dependency parameters. We then use the Akaike information criterion (AIC) to enforce model sparsity by incorporating only a minimum number of non-zero dependency parameters into the point process model based on a trade-off between model complexity and its prediction power. Using extensive numerical simulations, we show that our method (i) can correctly identify the functional dependencies and thus improve the prediction of spiking activity and (ii) can improve the prediction of spiking activity with significantly fewer number of parameters compared to when regularization is not enforced. Our approach may serve as a tool to investigate brain connectivity patterns across spatiotemporal scales.