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Flexible Modulated Poisson

Description: This code repository provides a MATLAB implementation of the flexible over-dispersed Poisson model in

"Dethroning the Fano Factor: a flexible, model-based approach to partitioning neural variability" published in Neural Computation, 2018. [link]

The models fit in this code base are modulated Poisson models where the data is described by the generative model

r = Poiss(f(x+n))

where x is the stimulus-related response, n is trial dependent noise that is normally distributed as

n ~ N(0,sigma^2)

and f() is a nonlinearity. The three possible nonlinearities in thiscode package are the exponential, soft-rectification and power-soft-rectification functions. The model fits the per-stimulus values x, the noise variance sigma^2 and the parameters of the nonlinearity using a Laplace approximation method.

Code desctiption:

The main file to use in this repository is

 negLfun_latentPoiss.m

which is a function that takes in a parameter set, event count data, and a handle to a link function and returns the negative log-likelihood value for that data. The intended use is to use this function in conjunction with fmincon.m or a similar optimization function in order to optimize the negative log-likelihood with respect to the parameter set.

Usage

• Launch matlab and cd into the flexibleModulatedPoisson directory.

• Examine the demo script demo.m for an example on the appropriate use of this function. demo.m generates a set of synthetic data that mimics the format of the data used in the related paper. It then demonstrates the correct use of the negLfun_latentPoiss.m function in fitting the three models included in the package. The results are then compared, showing how to extract the fit parameters correctly from the fminunc output, as some of the parameters are fit under an exponential transformation to ensure positivity.

Code download:

• Clone: clone the repository from github: git clone https://github.com/adamshch/flexibleModulatedPoisson.git

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