Sparse generalized Laguerre-Volterra model of neural population dynamics.

To understand the function of a brain region, e.g., hippocampus, it is necessary to model its input-output property. Such a model can serve as the computational basis of the development of cortical prostheses restoring the transformation of population neural activities performed by the brain region. We formulate a sparse generalized Laguerre-Volterra model (SGLVM) for the multiple-input, multiple-output (MIMO) transformation of spike trains. A SGLVM consists of a set of feedforward Laguerre-Volterra kernels, a feedback Laguerre-Volterra kernel, and a probit link function. The sparse model representation involving only significant self and cross terms is achieved through statistical model selection and cross-validation methods. The SGLVM is applied successfully to the hippocampal CA3-CA1 population dynamics.