Fast population coding (Huys et al. 2007)

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Accession:93394
"Uncertainty coming from the noise in its neurons and the ill-posed nature of many tasks plagues neural computations. Maybe surprisingly, many studies show that the brain manipulates these forms of uncertainty in a probabilistically consistent and normative manner, and there is now a rich theoretical literature on the capabilities of populations of neurons to implement computations in the face of uncertainty. However, one major facet of uncertainty has received comparatively little attention: time. In a dynamic, rapidly changing world, data are only temporarily relevant. Here, we analyze the computational consequences of encoding stimulus trajectories in populations of neurons. ..."
Reference:
1 . Huys QJ, Zemel RS, Natarajan R, Dayan P (2007) Fast population coding. Neural Comput 19:404-41 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Connectionist Network;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB;
Model Concept(s): Methods;
Implementer(s):
function [vps,mps,weight,ps] = psinf(id,time,sigma,lambda,tau,rw,s);
%
% PSINF.M
%
% This code is released in conjunction with the paper 
%
%	Huys QJM, Zemel RS, Natarajan R and Dayan P (2006): Fast population
%	coding Neural Computation
%	
% and can be downloaded from 
%
%	http://www.gatsby.ucl.ac.uk/~qhuys/code.html
%
% This function is called by GETINF.M. It computes the posterior at times at
% which a spike was observed.
%
% Copyright Quentin Huys 2006




Tsp = length(time);

dt = abs(repmat(time',1,Tsp)-repmat(time,Tsp,1));
if rw==0; 		C = lambda*exp(-.5*dt.^2/tau^2);
elseif rw==1; 		C = lambda.^dt*tau^2/(1-lambda^2);
end

Cll = C(1:end-1,1:end-1);
ClT = C(1:end-1,end);
CTl = C(1:end-1,end)';
CTT = C(end,end);

iC = inv( sigma^2*eye(size(Cll)) + Cll);

vps = 	inv( 1/(CTT-CTl*iC*ClT) + 1/sigma^2);
weight = vps*[1/(CTT-CTl*iC*ClT)*CTl*iC  1/sigma^2];

mps = weight*id';


ps = exp(-.5*(s'-mps).^2/vps -.5*log(2*pi*vps));