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KL_Rsquare_cazettes_IC_clean.m
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% This file computes some experiments and figures of Dehaene, Coen-Cagli,
% Pouget 2019
% This file computes KL divergence and R-square figures for the Cazettes IC
% model
%
% IMPORTANT: to run this file, please add to path (select both -> right click -> add to path -> selected folders and subfolders)
% the following two folders
% - maxent
% - lbfgs
clear all
FS=20; % Fontsize for figures
targetVar = true % If true, the uncertainty is defined as the posterior variance
% If false, the uncertainty is defined as the posterior
% entropy instead (as in the supplementary information)
load('OracleLlAndInfo_ProbTrainLRTSUM_3Batch2000_T01_BC1','NBC','Kf','Kt1','N','Nbatch')
modelnlin = 'LRTSUM';
% We pre-allocate key quantities for memory storage
KLneulin = zeros(NBC,1);
KLneunlin = KLneulin;
seKLneulin = zeros(NBC,2);
seKLneunlin = seKLneulin;
nboot=100;
Rsquare_Rlin = zeros(NBC,nboot);
Rsquare_Rnlin = Rsquare_Rlin;
Rsquare_RnlinProd = Rsquare_Rlin;
Rsquare_gRnlin = Rsquare_Rlin;
Rsquare_widthRnlin = Rsquare_Rlin;
Rsquare_gwidthRnlin = Rsquare_Rlin;
Rsquare_decodeRlin = Rsquare_Rlin;
Rsquare_decodeRnlin = Rsquare_Rlin;
%%%%%
% Main computational loop
% For every BC level, we compute a bunch of things
% oracle situation: we condition on a specific BC level
for indNBC=1:NBC
s = indNBC;
load(strcat('OracleLlAndInfo_ProbTrain',modelnlin,'_',num2str(N/Nbatch),'Batch',num2str(Nbatch),'_T01_BC',num2str(s)));
s = indNBC;
% load the Cazettes data
Rnlin = Rnlin3;
BAllnlin = BAllnlin3;
itdSubset = 5:7; % subselect the ITDs
KitdSubset = size(itdSubset,2);
LL = LL(:,:,itdSubset,:); %*** loglikelihood for just one true ITD
LLneulin=LL; % pre-allocate memory
LLneunlin=LL; % pre-allocate memory
Rlin = Rlin (:,:,itdSubset,:);
Rnlin = Rnlin(:,:,itdSubset,:);
% approximate decoding of the neuronal activity
% the weights are stored into the BAlllin variable and have been
% computed earlier
X = reshape(Rlin,[Kf*Kt1 KitdSubset*N])'; % removed inddt2
LLneulin(s,:,:,:) = reshape( energy(BAlllin,X)', [Kt1, KitdSubset, N]);
X = reshape(Rnlin,[Kf*Kt1 KitdSubset*N])'; % removed inddt2
LLneunlin(s,:,:,:) = reshape( energy(BAllnlin,X)', [Kt1, KitdSubset, N]);
% extract test set
% train set was used to construct the decoding weights earlier
LL = squeeze(LL(s,:,:,indtest));
LLneulin = squeeze(LLneulin (s,:,:,indtest));
LLneunlin = squeeze(LLneunlin(s,:,:,indtest));
Rlin = Rlin(:,:,:,indtest);
Rnlin = Rnlin(:,:,:,indtest);
% select all trials
indtri = 1:size(indtest,2);
NT = size(indtri,2);
%%% compute full posterior (w unif prior), per trial
tmp = nanmax(LL(:,indtri),[],1); % avoid infinities in the likelihood function
LL_norm = bsxfun(@minus,LL(:,indtri),tmp);
tmp = nanmax(LLneulin(:,indtri),[],1); % avoid infinities in the likelihood function
LLneulin_norm = bsxfun(@minus,LLneulin(:,indtri),tmp);
tmp = nanmax(LLneunlin(:,indtri),[],1); % avoid infinities in the likelihood function
LLneunlin_norm = bsxfun(@minus,LLneunlin(:,indtri),tmp);
% normalized posterior distributions
L_norm = bsxfun(@rdivide,exp(LL_norm),nansum(exp(LL_norm),1)); % compute likelihood
Lneulin_norm = bsxfun(@rdivide,exp(LLneulin_norm),nansum(exp(LLneulin_norm),1));
Lneunlin_norm = bsxfun(@rdivide,exp(LLneunlin_norm),nansum(exp(LLneunlin_norm),1));
%%% compute KL divergence between true and reconstructed posterior
NDT2 = size(L_norm,1);
doeps=1;
tDenom = diag(L_norm'*(log(L_norm+eps*doeps)-log(ones(NDT2,NT)/NDT2)));
tKLneulin = diag(L_norm'*(log(L_norm+eps*doeps)-log(Lneulin_norm+eps*doeps))) ./ tDenom;
tKLneunlin = diag(L_norm'*(log(L_norm+eps*doeps)-log(Lneunlin_norm+eps*doeps))) ./ tDenom;
KLneulin(s) = nanmedian(tKLneulin);
KLneunlin(s) = nanmedian(tKLneunlin);
nboot1=1000;
seKLneulin(s,:) = bootci(nboot1,{@nanmedian,tKLneulin},'type','bca');
seKLneunlin(s,:) = bootci(nboot1,{@nanmedian,tKLneunlin},'type','bca');
%%% compute posterior width
x=deltaTrue(1:end);
muL = x*L_norm;
varL = sum(L_norm.*(repmat(x',1,size(L_norm,2))-repmat(muL,numel(x),1)).^2);
ivarL = 1./varL;
muL = x*Lneulin_norm;
varL = sum(Lneulin_norm.*(repmat(x',1,size(Lneulin_norm,2))-repmat(muL,numel(x),1)).^2);
ivarLneulin = 1./varL;
muL = x*Lneunlin_norm;
varL = sum(Lneunlin_norm.*(repmat(x',1,size(Lneunlin_norm,2))-repmat(muL,numel(x),1)).^2);
ivarLneunlin = 1./varL;
%%% compute entropy
entropyL = - diag( L_norm' * log(L_norm) ); % the diagonal of U^T U corresponds to a sum
entropyLneulin = - diag( Lneulin_norm' * log(Lneulin_norm) );
entropyLneunlin = - diag( Lneunlin_norm' * log(Lneunlin_norm) );
%%% extract features from population activity (width, gain) to correlate with uncertainty; also, single neuron tuning curve width and gain
tRlin = reshape( Rlin (:,:,:,indtri), [Kf, Kt1, KitdSubset * NT] ); % removed inddt2
tRnlin = reshape( Rnlin(:,:,:,indtri), [Kf, Kt1, KitdSubset * NT] ); % removed inddt2
muRlin = zeros(Kf,KitdSubset*NT);
widthRlin = zeros(Kf,KitdSubset*NT);
muRnlin = zeros(Kf,KitdSubset*NT);
widthRnlin = zeros(Kf,KitdSubset*NT);
gwidthRnlin = zeros(Kf,KitdSubset*NT);
gRnlin = zeros(Kf,KitdSubset*NT);
for f=1:Kf
%%% population, per trial
tmp = squeeze(tRlin(f,:,:));
tmp = bsxfun(@minus,tmp,nanmin(tmp,[],1));
tmpnorm = bsxfun(@rdivide,tmp,nansum(tmp,1));
muRlin(f,:) = x*tmpnorm;
widthRlin(f,:) = sum(tmpnorm.*bsxfun(@minus,x',muRlin(f,:)).^2);
tmp = squeeze(tRnlin(f,:,:));
gRnlin(f,:) = nansum(tmp);
tmpnorm = bsxfun(@rdivide,tmp,nansum(tmp,1));
muRnlin(f,:) = x*tmpnorm;
widthRnlin(f,:) = sum(tmpnorm.*bsxfun(@minus,x',muRnlin(f,:)).^2);
gwidthRnlin(f,:) = gRnlin(f,:)./widthRnlin(f,:);
end
%%% population, per trial
tmp = squeeze(sum(tRlin));
tmp = bsxfun(@minus,tmp,nanmin(tmp,[],1));
tmpnorm = bsxfun(@rdivide,tmp,nansum(tmp,1));
mutmp = x*tmpnorm;
widthRlinSum = sum(tmpnorm.*bsxfun(@minus,x',mutmp).^2);
tmp = squeeze(sum(tRnlin));
gRnlinSum = sum(tmp);
tmp = bsxfun(@minus,tmp,nanmin(tmp,[],1));
tmpnorm = bsxfun(@rdivide,tmp,nansum(tmp,1));
mutmp = x*tmpnorm;
widthRnlinSum = sum(tmpnorm.*bsxfun(@minus,x',mutmp).^2);
%%% Define the target of the regression
if targetVar
%%% Target log of certainty
ivarL = log(ivarL);
ivarLneulin = log(ivarLneulin);
ivarLneunlin = log(ivarLneunlin);
else
%%% Target the log entropy
ivarL = log(entropyL)';
ivarLneulin = log(entropyLneulin)';
ivarLneunlin = log(entropyLneunlin)';
end
%%% take log of inverse of population width
widthRlin = log(1./widthRlin);
widthRnlin = log(1./widthRnlin);
%%% take log of population gain
gRnlin = log(gRnlin);
gwidthRnlin = log(gwidthRnlin);
%%% compute R-square of true certainty vs reconstruction from poulation features (ENCODING)
NTT = NT;
NTtr = round(4*NTT/5);
NTte = numel(NTtr+1:NTT);
for k=1:nboot
indperm = randperm(NT);
indtr = indperm(1:NTtr);
indte = indperm((1+NTtr):end);
tmp=reshape(tRlin(:,:,indtr),Kf*Kt1,NTtr); %*** LINEAR
tmp1=reshape(tRlin(:,:,indte),Kf*Kt1,NTte);
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_Rlin(s,k) = (1-sum((ivarL(indte)'-[tmp1' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
tmp=reshape(tRnlin(:,:,indtr),Kf*Kt1,NTtr); %*** LRTSUM
tmp1=reshape(tRnlin(:,:,indte),Kf*Kt1,NTte);
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_Rnlin(s,k) = (1-sum((ivarL(indte)'-[tmp1' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
tmp1=reshape(tRnlin(:,:,indtr),Kf*Kt1,NTtr); %*** LRTSUM, product of activities
Kneu = Kf*Kt1;
Kneusq = (Kneu^2+Kneu)/2;
tmp = NaN(Kneusq,NTtr);
for nt = 1:NTtr
tmpmat = tmp1(:,nt)*tmp1(:,nt)';
tmp(:,nt) = tmpmat(logical(tril(ones(Kneu))));
end
tmp1=reshape(tRnlin(:,:,indte),Kf*Kt1,NTte);
testRnlinProd = NaN(Kneusq,NTte);
for nt = 1:NTte
tmpmat = tmp1(:,nt)*tmp1(:,nt)';
testRnlinProd(:,nt) = tmpmat(logical(tril(ones(Kneu))));
end
if NTtr<=Kneusq
indsub = randperm(Kneusq);
tmp = tmp(indsub(1:round(NTtr/2)),:);
testRnlinProd = testRnlinProd(indsub(1:round(NTtr/2)),:);
end
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_RnlinProd(s,k) = (1-sum((ivarL(indte)'-[testRnlinProd' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
tmp=gRnlin(:,indtr);
tmp1=gRnlin(:,indte);
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_gRnlin(s,k) = (1-sum((ivarL(indte)'-[tmp1' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
tmp=widthRnlin(:,indtr);
tmp1=widthRnlin(:,indte);
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_widthRnlin(s,k) = (1-sum((ivarL(indte)'-[tmp1' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
tmp=gwidthRnlin(:,indtr);
tmp1=gwidthRnlin(:,indte);
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_gwidthRnlin(s,k) = (1-sum((ivarL(indte)'-[tmp1' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
if 0 %%% compute R-square of true certainty vs reconstruction from poulation activtiy (DECODING) ***with*** linear fit
tmp=ivarLneulin(indtr);
tmp1=ivarLneulin(indte);
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_decodeRlin(s,k) = (1-sum((ivarL(indte)'-[tmp1' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
tmp=ivarLneunlin(indtr);
tmp1=ivarLneunlin(indte);
B = regress(ivarL(indtr)',[tmp' ones(NTtr,1)]);
Rsquare_decodeRnlin(s,k) = (1-sum((ivarL(indte)'-[tmp1' ones(NTte,1)]*B).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
else %%% compute R-square of true certainty vs reconstruction from poulation activtiy (DECODING) ***without*** linear fit
Rsquare_decodeRlin(s,k) = (1-sum((ivarL(indte)-ivarLneulin(indte)).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
Rsquare_decodeRnlin(s,k) = (1-sum((ivarL(indte)-ivarLneunlin(indte)).^2)/sum((ivarL(indte)-mean(ivarL(indte))).^2));
end
end
end
%%%%%
% All computations are complete: now we plot the figures
%myerrorbar = @(x,y,z,a,b) errorbar(x,y,y - z(:,1),z(:,2)-y);
%%% plot KL vs BC
figure;
hold on; axis square;
myerrorbar(BinCorLabel',KLneunlin,seKLneunlin,[.6 .6 .6],1);
plot(BinCorLabel',KLneunlin,'-k');
xlabel('BC','FontSize',FS)
ylabel('KL','FontSize',FS)
set(gca,'YLim',[0 .15],'YTick',[0:.01:0.1],'YTickLabel',100*[0:.01:0.1])
%%% plot Rsquare vs BC
figure;
alpha=0.01;
nboot2=1000;
shade=1;
hold on; axis square;
% myerrorbar(BinCorLabel,nanmedian(Rsquare_decodeRlin'),bootci(nboot2,{@nanmedian,Rsquare_decodeRlin'},'alpha',alpha)','k',shade);
myerrorbar(BinCorLabel',nanmedian(Rsquare_RnlinProd')', bootci(nboot2,{@nanmedian,Rsquare_RnlinProd'}, 'alpha',alpha)','m',shade);
myerrorbar(BinCorLabel',nanmedian(Rsquare_gwidthRnlin')', bootci(nboot2,{@nanmedian,Rsquare_gwidthRnlin'}, 'alpha',alpha)','y',shade);
myerrorbar(BinCorLabel',nanmedian(Rsquare_Rnlin')', bootci(nboot2,{@nanmedian,Rsquare_Rnlin'}, 'alpha',alpha)','b',shade);
myerrorbar(BinCorLabel',nanmedian(Rsquare_gRnlin')', bootci(nboot2,{@nanmedian,Rsquare_gRnlin'}, 'alpha',alpha)','r',shade);
myerrorbar(BinCorLabel',nanmedian(Rsquare_widthRnlin')', bootci(nboot2,{@nanmedian,Rsquare_widthRnlin'}, 'alpha',alpha)','g',shade);
myerrorbar(BinCorLabel',nanmedian(Rsquare_decodeRnlin')', bootci(nboot2,{@nanmedian,Rsquare_decodeRnlin'}, 'alpha',alpha)','k',shade);
legend({'Generalized Gain + Product (??)','Gain / Width Ratio (??)','Generalized Gain (??)','Gain (??)','Width (??)','Decoding (??)',})
xlabel('BC','FontSize',FS)
ylabel('Rsquare(certainty)')
set(gca,'YLim',[0 1],'YTick',[0:.2:1])