Simple tutorial on Gaussian and Poisson generalized linear models (GLMs) for spike train data, written in python.
Author: Jesse Kaminsky. (Translated from a Matlab version prepared by Jonathan Pillow).
Slides: This tutorial was prepared for use in a "Short Course" on Data Science and Data Skills for Neuroscientists organized at the SFN 2016 meeting. The slides used during the 1-hour presentation are available here.
Dataset: A small dataset required for the tutorial (provided by EJ Chichilnisky) is provided in the directory data_RGCs.
Description: The tutorial contains five jupyter notebooks that cover various methods for fitting and analyzing Gaussian and Poisson regression models for spike train data. Each notebook an interactive, self-contained script with 'blocks' of code that demonstrate each step in the fitting / analysis / model comparison pipeline:
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tutorial1_PoissonGLM.ipynb - 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.
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tutorial2_spikehistcoupledGLM.ipynb - 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).
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tutorial3_regularization_linGauss.ipynb - 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").
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tutorial4_regularization_PoissonGLM.ipynb - MAP estimation of Poisson-GLM parameters using same two priors considered in tutorial3.
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tutorial5_MAPdecoding.ipynb - Bayesian (MAP) decoding of the stimulus from spikes under a fitted Poisson GLM (with or without spike-history). (Note: this tutorial was added by J. Kaminsky, and does not exist in the Matlab version)
Citation: If you wish to cite this tutorial, feel free to acknowledge the paper from which it developed: Pillow et al, Nature 2008. Or, for the MAP decoding tutorial, cite: Pillow et al, Neural Comp 2011.
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:
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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.
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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.