Fisher and Shannon information in finite neural populations (Yarrow et al. 2012)

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Here we model populations of rate-coding neurons with bell-shaped tuning curves and multiplicative Gaussian noise. This Matlab code supports the calculation of information theoretic (mutual information, stimulus-specific information, stimulus-specific surprise) and Fisher-based measures (Fisher information, I_Fisher, SSI_Fisher) in these population models. The information theoretic measures are computed by Monte Carlo integration, which allows computationally-intensive decompositions of the mutual information to be computed for relatively large populations (hundreds of neurons).
1 . Yarrow S, Challis E, Seri├Ęs P (2012) Fisher and Shannon information in finite neural populations. Neural Comput 24:1740-80 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Connectionist Network;
Brain Region(s)/Organism: Unknown;
Cell Type(s):
Gap Junctions:
Simulation Environment: MATLAB;
Model Concept(s): Rate-coding model neurons;
Implementer(s): Yarrow, Stuart [s.yarrow at];
function [fisher, ssi, SSIfisher] = fig8(N, beta, sigma_mod, sigma)
% fig8  Reproduce curves from Figure 8
% [fisher, ssi, SSIfisher] = fig8(N, adapt, sigma_adapt, sigma) calculates the
% population Fisher information, SSI and SSI_Fisher for:
% population size N
% adaptation modulation factor beta (in range [0,1])
% adaptation width sigma_mod (degrees)
% tuning curve width sigma (degrees)

% Stuart Yarrow - 18/11/2011


stderr = 5e-3;      % Target relative error for MC halting
maxiter = 2e3;      % MC iteration limit

fTau = 5.0;         % variability F/tau (spikes/s^2)
tau = 1.0;          % integration time (s)
F = fTau .* tau;    % Fano factor
fbg = 10.0;         % background activity (spikes/s)
alpha = 0.5;        % variability exponent
fmax = 50.0;        % peak firing rate (spikes/s)

% Preferred stimuli
nrns = [-180 : 360/N : 180-360/N];

% Define stimulus ensemble and population
stim = StimulusEnsemble('circular', 360, 360);
popNrns = CircGaussNeurons(nrns, sigma, fmax, fbg, tau, 'Gaussian-independent', [F alpha]);

% Apply gain modulation
popNrns = popNrns.gainadapt(sigma_mod, beta, 0.0);

% Compute measures
fisher = popNrns.fisher('analytic', stim, 0.0);
SSIfisher =  popNrns.SSIfisher([], 'analytic', stim, 0.0);
ssi = popNrns.ssiss([], 'randMC', stim, [], stderr, maxiter, 1e10);

% Report results
plot(stim.ensemble, fisher./max(fisher), 'r--', stim.ensemble, ssi./max(ssi), 'k-', stim.ensemble, SSIfisher./max(SSIfisher), 'b:')
title(sprintf('fig8.m\nParameters: N = %d, \\beta = %g, \\sigma_{mod} = %g^\\circ, \\sigma = %g^\\circ\n', N, beta, sigma_mod, sigma))
xlabel('Stimulus angle \theta')
ylabel('Information (normalised)')
legend({'Fisher information' 'SSI' ' SSI_{Fisher}'})

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