Multiscale modeling of dependencies between spikes and fields

Measuring and modeling the brain at multiple spatiotemporal scales are important for studying brain function and developing high-performance brain-machine interfaces. To better understand neural encoding of behavior, the conditional dependencies between different scales of brain activity should be considered in the multiscale modeling framework. Here, we develop a new multiscale model that characterizes the conditional dependence between spikes and fields during behavior. We modeled this mutual dependence by incorporating the effect of field features on each neuron's firing rate function. To reduce the number of model parameters to be learned, we assumed that the strength of dependency between a pair of neuron and field feature is a function of the distance between electrodes from which they are recorded. We then constructed the shape of this unknown spatial dependency function with a weighted sum of Gaussian kernels. We devised an unsupervised learning algorithm using expectation-maximization to learn the kernel weights as well as other model parameters. Using simulated data, we show that this learning algorithm accurately identifies the multiscale model parameters and the conditional dependency functions. This modeling and learning framework can help study spike-field encoding and dependencies and could enhance future neurotechnologies.