A central goal of computational neuroscience is to understand the neural code, the semantic relationship between neural spike trains and the extrinsic (sensory, motor, & cognitive) variables that they represent. One powerful approach to this problem involves "cascade" point process models, which describe the neural encoding process in terms of a cascade of three stages: (1) linear dimensionality-reduction of a high-dimensional stimulus space; (2) a nonlinear transformation from feature space to spike rate; and (3) an inhomogeneous, conditional renewal (e.g., Poisson) spiking process. These models have been shown to provide accurate descriptions of single- and multi-neuron spike responses in a wide variety of brain areas, and have shed light on the fundamental units (rates, spike times, correlations, oscillations) that neurons use to convey information. Recent innovations have focused on extending these models to incorporate richer nonlinear dependencies and dynamics, and to capture more biologically realistic features of neural spike trains.

In this tutorial, I will provide a general introduction to cascade neural encoding models and then discuss some more recent advances, including models for non-Poisson spike trains and correlated neural population responses. Topics will include: Poisson & renewal processes, reverse correlation, spike-triggered average / covariance (STA/STC) analysis, inverse regression, maximally informative dimensions (MID), generalized linear models (GLMs), Ising models, latent variable / shared-noise models, functional connectivity, advanced regularization methods, and model-based (Bayesian) techniques for decoding multi-neuron spike trains.