LNPfitting

Linear-Nonlinear-Poisson (LNP) model fitting via maximum likelihood, aka Maximally-Informative-Dimensions (MID) in Matlab.

Description: Estimates the parameters of an LNP model from a stimulus and spike train using the maximally informative dimension (MID) estimator (introduced in Sharpee et al 2004). The LNP model model parameters consist of

• a bank of (one or more) linear filters that perform dimensionality reduction
• a nonlinear function that maps filter outputs to instantaneous spike rate

As shown in Williamson et al 2015, MID is a maximum likelihood estimator for the LNP model with a nonparametric (histogram-based) model for the nonlinearity.

Relevant publications:

• Sharpee, Rust, & Bialek, Neural Computation 2004 (original publication).
• Williamson, Sahani, & Pillow, PLoS Comp Bio 2015. [abs, pdf, link]

Download

• Download: zipped archive LNPfitting-master.zip
• Clone: clone the repository from github: git clone git@github.com:pillowlab/LNPfitting.git

Usage

• Launch matlab and cd into the directory containing the code (e.g. cd code/LNPfitting/).

• Examine the demo scripts for annotated example analyses of simulated datasets:

  • demo1_1temporalfilter.m - estimate a single temporal filter using STA, iSTAC, GLM with exponential nonlinearity, and using ML / MID estimation of filter and a nonlinearity parametrized by radial basis functions. Shows validation using R^2 of true filter and single-spike information (log-likelihood).
  • demo2_2temporalfilters.m - similar, but for two-filter LNP models; shows how to plot inferred 2D nonlinearity.
  • demo3_3temporalfilters - compares iSTAC, and ML/MID estimates with cylindrical basis functions (CBFs) and with radial basis functions (RBFs) for parametrizing the nonlinearity.
  • demo4_1spacetimefilter.m - similar to demo1 but for 2D (space x time) binary white noise stimulus.
  • demo5_5spacetimefilters.m - similar to demo3, but recovers 5 space-time filters. Compares iSTAC, and ML/MID with CBFs and RBFs.

Notes

Primary differences between our implementation and that of Sharpee et al 2004:

• Parametrizes the nonlinearity with smooth RBF (or CBF) basis functions (followed by a rectifying point nonlinearity to keep spike rates positive) instead of square histogram bins. This makes the log-likelihood differentiable and therefore easier to ascend.

• Uses standard quasi-Newton optimization methods (fminunc or minFunc) instead of simulated annealing. (Thus no guarantee that it finds global optimum, but runtime is substantially faster and performance is high in simulated and real datasets considered so far).