Simple tutorial on Gaussian and Poisson generalized linear models (GLMs) for spike train data.
author: Jonathan Pillow, Nov 2016.

This tutorial were prepared for the Society for Neuroscience 2016 "Short Course" on Data Science and Data Skills for Neuroscientists, held in San Diego in Nov, 2016. The slides used during the 1-hour short course presentation are available in the "slides" directory. A small dataset required for the tutorial is available here.

The tutorial is broken into four pieces which aim to introduce methods for fitting and simulating Gaussian and Poisson regression models for spike train data. Each is an interactive, self-contained script with 'blocks' of code that demonstrate each step in the fitting / analysis / model comparison pipeline:

• tutorial1_PoissonGLM.m - illustrates the fitting of a linear-Gaussian GLM (also known as the 'linear least-squares regression model') and a Poisson GLM (aka 'linear-nonlinear-Poisson' model) to single retinal ganglion cell responses to a temporal white noise stimulus.

• tutorial2_spikehistcoupledGLM.m - fitting of an autoregressive Poisson GLM (i.e., a GLM with spike-history) and a multivariate autoregressive Poisson GLM (a GLM with spike-history AND coupling between neurons).

• tutorial3_regularization_linGauss.m - regularizing linear-Gaussian model parameters using maximum a posteriori (MAP) estimation under two kinds of priors:

  • (1) ridge regression (aka "L2 penalty");
  • (2) L2 smoothing prior (aka "graph Laplacian").

• tutorial4_regularization_PoissonGLM.m - MAP estimation of Poisson-GLM parameters using same two priors considered in tutorial3.

Relevance / comparison to other GLM packages:

This tutorial is designed primarily for pedagogical purposes. The tutorial scripts are (almost entirely) self-contained, making it easy to understand the basic steps involved in simulating and fitting. It is easy to alter these scripts (e.g., to incorporate different kinds of regressors, or different kinds of priors for regularization). However, this implementation is not memory-efficient and does not support some of the advanced features available in other GLM packages (e.g., smooth basis functions for spike-history filters, memory-efficient temporal convolutions, different timescales for stimulus and spike-history components, low-rank parametrization of spatio-temporal filters, flexible handling of trial-based data). For more advanced features and applications, see the following two repositories:

• neuroGLM - designed for single-neuron, trial-structured data. Supports flexible design matrices with multiple types of regressors. Relevant pub: Park et al, Nat Neurosci 2014.

• GLMspiketools - designed for single- and multi-neuron spike trains with flexible nonlinearities, multiple timescales, and low-rank parametrization of filters. Relevant pub: Pillow et al, Nature 2008.