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Copy pathMCMC_MaxCal_Ising.m
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333 lines (300 loc) · 9.27 KB
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%Jij will be 40 neurons and 4 time steps, so a 160x160 matrix
%it will be stacked, neurons 1 2... of first time then second time, etc.
%% initialize ground truth. This is stochastic, so the produced data will
%not be identical to the attached data.
N=40;
T=4;
J=zeros(N*T);
MJ=.015;
sigJ=.015;
a=4;
s0=randi(2,N*T,1);
s0=s0-1;
s0=2*s0-1; %either +1 or -1
Equiltime=5000;
Corrtime=500;
Numtime=500000;
for t=1:T
for s=1:t-1
for i=1:N
for j=1:N
J((t-1)*N+i,(s-1)*N+j)=(randn*sigJ*a^(-abs(t-s))+MJ*a^(-abs(t-s)));
end
J((t-1)*N+i,(s-1)*N+i)=20*MJ*a^(-abs(t-s));
end
end
end
J=J+J';
for t=1:T
for i=1:N
for j=1:i-1
J((t-1)*N+i,(t-1)*N+j)=randn*sigJ+MJ;
J((t-1)*N+j,(t-1)*N+i)=J((t-1)*N+i,(t-1)*N+j);
end
end
end
h=-.1*ones(N*T,1);
%% simulate ground truth to extract means and correlations
[Havg,FM,SM,~]=MCMC(J,h,N*T,s0,Equiltime,Corrtime,Numtime); %Using MCMC.m
CC=SM-FM*FM';
FFM=FM;
%% calculate LC estimates, Eq. 7.
hUC=zeros(N*T,1);
JLC=-inv(CC);
for k=1:N*T
JLC(k,k)=0;
end
%% Solves the Uncoupled problem exactly, Eq. 5
pH=@(L,s1,s2,s3,s4) exp(L(1).*s1+L(2).*s2+L(3).*s3+L(4).*s4+L(5).*s1.*s2+L(6).*s1.*s3+L(7).*s1.*s4+L(8).*s2.*s3+L(9).*s2.*s4+L(10).*s3.*s4);
logZ=@(L) log(pH(L,1,1,1,1)+pH(L,1,1,1,-1)+pH(L,1,1,-1,1)+pH(L,1,1,-1,-1)+pH(L,1,-1,1,1)+pH(L,1,-1,1,-1)+pH(L,1,-1,-1,1)+pH(L,1,-1,-1,-1)+pH(L,-1,1,1,1)+pH(L,-1,1,1,-1)+pH(L,-1,1,-1,1)+pH(L,-1,1,-1,-1)+pH(L,-1,-1,1,1)+pH(L,-1,-1,1,-1)+pH(L,-1,-1,-1,1)+pH(L,-1,-1,-1,-1));
JUC=zeros(N*T,N*T);
for i=1:N
S=@(L) logZ(L)-L(1)*FM(i)-L(2)*FM(N+i)-L(3)*FM(2*N+i)-L(4)*FM(3*N+i)-L(5)*SM(i,N+i)-L(6)*SM(i,2*N+i)-L(7)*SM(i,3*N+i)-L(8)*SM(N+i,2*N+i)-L(9)*SM(N+i,3*N+i)-L(10)*SM(2*N+i,3*N+i);
L0=zeros(10,1);
options=optimset('MaxIter',10000,'MaxFunEvals',10000);
LL=fminsearch(S,L0,options);
LL=fminsearch(S,LL,options);
hUC(i)=LL(1);
hUC(N+i)=LL(2);
hUC(2*N+i)=LL(3);
hUC(3*N+i)=LL(4);
JLC(N+i,i)=LL(5);
JUC(N+i,i)=LL(5);
JLC(2*N+i,i)=LL(6);
JUC(2*N+i,i)=LL(6);
JLC(3*N+i,i)=LL(7);
JUC(3*N+i,i)=LL(7);
JLC(2*N+i,N+i)=LL(8);
JUC(2*N+i,N+i)=LL(8);
JLC(3*N+i,N+i)=LL(9);
JUC(3*N+i,N+i)=LL(9);
JLC(3*N+i,2*N+i)=LL(10);
JUC(3*N+i,2*N+i)=LL(10);
JLC(i,N+i)=JLC(N+i,i);
JUC(i,N+i)=JUC(N+i,i);
JLC(i,2*N+i)=JLC(2*N+i,i);
JUC(i,2*N+i)=JUC(2*N+i,i);
JLC(i,3*N+i)=JLC(3*N+i,i);
JUC(i,3*N+i)=JUC(3*N+i,i);
JLC(N+i,2*N+i)=JLC(2*N+i,N+i);
JUC(N+i,2*N+i)=JUC(2*N+i,N+i);
JLC(N+i,3*N+i)=JLC(3*N+i,N+i);
JUC(N+i,3*N+i)=JUC(3*N+i,N+i);
JLC(2*N+i,3*N+i)=JLC(3*N+i,2*N+i);
JUC(2*N+i,3*N+i)=JUC(3*N+i,2*N+i);
end
%% Calculate LC corrections to h using the mean-field equation. Eq. 6.
hLC=zeros(N*T,1);
for i=1:N
for t=1:T
hLC((t-1)*N+i)=hUC((t-1)*N+i);
for j=1:N
if j~=i
for s=1:T
hLC((t-1)*N+i)=hLC((t-1)*N+i)-JLC((t-1)*N+i,(s-1)*N+j)*FM((s-1)*N+j);
end
end
end
end
end
%% Plot estimates vs ground truth, commented to suppress output
Joffdiag=JLC-JUC;
JJ=reshape(J,[N*N*T*T,1]);
JJP=reshape(JLC,[N*N*T*T,1]);
JJO=reshape(Joffdiag,[N*N*T*T,1]);
Iod=find(JJO~=0);
%scatter(JJ(Iod),JJP(Iod))
%scatter(JJ,JJP);
% JJod=JJ(Iod);
% JJPod=JJP(Iod);
% csvwrite('Brain_K_pair.txt',[JJod,JJPod])
% Id=find(JJO==0);
% JJd=JJ(Id);
% JJPd=JJP(Id);
% csvwrite('Brain_K_self.txt',[JJd,JJPd])
% csvwrite('Brain_h_neg_point_1.txt',[hPlef])
%% Calculate dynamics and synchrony for UC/LC vs ground truth vs just UC
Time=20000;
EQtime=500;
s=zeros(N,Time+EQtime+T);
R=randi(2,N,T);
R=R-1;
R=2*R-1; %either +1 or -1
s(:,1:T)=R;
htemp=zeros(N,1);
Jtemp=J(3*N+1:4*N,3*N+1:4*N);
for tt=T+1:Time+EQtime+T
for i=1:N
htemp(i)=h(3*N+i);
for j=1:N
for ss=1:T-1
htemp(i)=htemp(i)+J((ss-1)*N+j,3*N+i)*s(j,tt-T+ss);
end
end
end
[~,FM]=MCMC(Jtemp,htemp,N,s(:,tt-1),1000,1,1);
s(:,tt)=FM;
end
M=mean(s);
htemp=zeros(N,1);
Jtemp=JLC(3*N+1:4*N,3*N+1:4*N);
for tt=T+1:Time+EQtime+T
for i=1:N
htemp(i)=hLC(3*N+i);
for j=1:N
for ss=1:T-1
htemp(i)=htemp(i)+JLC((ss-1)*N+j,3*N+i)*s(j,tt-T+ss);
end
end
end
[~,FM]=MCMC(Jtemp,htemp,N,s(:,tt-1),1000,1,1);
s(:,tt)=FM;
end
MLC=mean(s);
htemp=zeros(N,1);
Jtemp=JUC(3*N+1:4*N,3*N+1:4*N);
for tt=T+1:Time+EQtime+T
for i=1:N
htemp(i)=hUC(3*N+i);
for j=1:N
for ss=1:T-1
htemp(i)=htemp(i)+JUC((ss-1)*N+j,3*N+i)*s(j,tt-T+ss);
end
end
end
[~,FM]=MCMC(Jtemp,htemp,N,s(:,tt-1),1000,1,1);
s(:,tt)=FM;
end
MUC=mean(s);
% csvwrite('Brain_time_series.txt',[M',MMF',MPlef'])
%% Calculate synchrony variances to see how our estimates change with
%temperature (interaction strength)
%This takes a long time to run. Be wary. We attach the output just in
%case
beta=.1:.005:1.25;
varb=zeros(length(beta),3); %first column is truth, second is MF+LR, third is just MF
magb=zeros(length(beta),3);
for l=300:length(beta)
Jb=beta(l)*J;
hb=beta(l)*h;
[Havg,FMb,SMb,~]=MCMC(Jb,hb,N*T,s0,Equiltime,Corrtime,Numtime);
CCb=SMb-FMb*FMb';
FFMb=FMb;
hUCb=zeros(N*T,1);
JLCb=-inv(CCb);
for k=1:N*T
JLCb(k,k)=0;
end
pH=@(L,s1,s2,s3,s4) exp(L(1).*s1+L(2).*s2+L(3).*s3+L(4).*s4+L(5).*s1.*s2+L(6).*s1.*s3+L(7).*s1.*s4+L(8).*s2.*s3+L(9).*s2.*s4+L(10).*s3.*s4);
logZ=@(L) log(pH(L,1,1,1,1)+pH(L,1,1,1,-1)+pH(L,1,1,-1,1)+pH(L,1,1,-1,-1)+pH(L,1,-1,1,1)+pH(L,1,-1,1,-1)+pH(L,1,-1,-1,1)+pH(L,1,-1,-1,-1)+pH(L,-1,1,1,1)+pH(L,-1,1,1,-1)+pH(L,-1,1,-1,1)+pH(L,-1,1,-1,-1)+pH(L,-1,-1,1,1)+pH(L,-1,-1,1,-1)+pH(L,-1,-1,-1,1)+pH(L,-1,-1,-1,-1));
JUCb=zeros(N*T,N*T);
for i=1:N
S=@(L) logZ(L)-L(1)*FMb(i)-L(2)*FMb(N+i)-L(3)*FMb(2*N+i)-L(4)*FMb(3*N+i)-L(5)*SMb(i,N+i)-L(6)*SMb(i,2*N+i)-L(7)*SMb(i,3*N+i)-L(8)*SMb(N+i,2*N+i)-L(9)*SMb(N+i,3*N+i)-L(10)*SMb(2*N+i,3*N+i);
L0=zeros(10,1);
options=optimset('MaxIter',10000,'MaxFunEvals',10000);
LL=fminsearch(S,L0,options);
LL=fminsearch(S,LL,options);
hUCb(i)=LL(1);
hUCb(N+i)=LL(2);
hUCb(2*N+i)=LL(3);
hUCb(3*N+i)=LL(4);
JLCb(N+i,i)=LL(5);
JUCb(N+i,i)=LL(5);
JLCb(2*N+i,i)=LL(6);
JUCb(2*N+i,i)=LL(6);
JLCb(3*N+i,i)=LL(7);
JUCb(3*N+i,i)=LL(7);
JLCb(2*N+i,N+i)=LL(8);
JUCb(2*N+i,N+i)=LL(8);
JLCb(3*N+i,N+i)=LL(9);
JUCb(3*N+i,N+i)=LL(9);
JLCb(3*N+i,2*N+i)=LL(10);
JUCb(3*N+i,2*N+i)=LL(10);
JLCb(i,N+i)=JLCb(N+i,i);
JUCb(i,N+1)=JUCb(N+i,i);
JLCb(i,2*N+i)=JLCb(2*N+i,i);
JUCb(i,2*N+i)=JUCb(2*N+i,i);
JLCb(i,3*N+i)=JLCb(3*N+i,i);
JUCb(i,3*N+i)=JUCb(3*N+i,i);
JLCb(N+i,2*N+i)=JLCb(2*N+i,N+i);
JUCb(N+i,2*N+i)=JUCb(2*N+i,N+i);
JLCb(N+i,3*N+i)=JLCb(3*N+i,N+i);
JUCb(N+i,3*N+i)=JUCb(3*N+i,N+i);
JLCb(2*N+i,3*N+i)=JLCb(3*N+i,2*N+i);
JUCb(2*N+i,3*N+i)=JUCb(3*N+i,2*N+i);
end
hLCb=zeros(N*T,1);
for i=1:N
for t=1:T
hLCb((t-1)*N+i)=hUCb((t-1)*N+i);
for j=1:N
if j~=i
for s=1:T
hLCb((t-1)*N+i)=hLCb((t-1)*N+i)-JLCb((t-1)*N+i,(s-1)*N+j)*FMb((s-1)*N+j);
end
end
end
end
end
Time=500000;
EQtime=500;
s=zeros(N,Time+EQtime+T);
R=randi(2,N,T);
R=R-1;
R=2*R-1;
s(:,1:T)=R;
htemp=zeros(N,1);
Jtemp=Jb(3*N+1:4*N,3*N+1:4*N);
for tt=T+1:Time+EQtime+T
for i=1:N
htemp(i)=hb(3*N+i);
for j=1:N
for ss=1:T-1
htemp(i)=htemp(i)+Jb((ss-1)*N+j,3*N+i)*s(j,tt-T+ss);
end
end
end
[~,FMb]=MCMC(Jtemp,htemp,N,s(:,tt-1),100,1,1);
s(:,tt)=FMb;
end
Mb=mean(s);
varb(l,1)=var(Mb);
magb(l,1)=mean(Mb);
htemp=zeros(N,1);
Jtemp=JLCb(3*N+1:4*N,3*N+1:4*N);
for tt=T+1:Time+EQtime+T
for i=1:N
htemp(i)=hLCb(3*N+i);
for j=1:N
for ss=1:T-1
htemp(i)=htemp(i)+JLCb((ss-1)*N+j,3*N+i)*s(j,tt-T+ss);
end
end
end
[~,FMb]=MCMC(Jtemp,htemp,N,s(:,tt-1),100,1,1);
s(:,tt)=FMb;
end
MLCb=mean(s);
varb(l,2)=var(MLCb);
magb(l,2)=mean(MLCb);
htemp=zeros(N,1);
Jtemp=JUCb(3*N+1:4*N,3*N+1:4*N);
for tt=T+1:Time+EQtime+T
for i=1:N
htemp(i)=hUCb(3*N+i);
for j=1:N
for ss=1:T-1
htemp(i)=htemp(i)+JUCb((ss-1)*N+j,3*N+i)*s(j,tt-T+ss);
end
end
end
[~,FMb]=MCMC(Jtemp,htemp,N,s(:,tt-1),100,1,1);
s(:,tt)=FMb;
end
MUCb=mean(s);
varb(l,3)=var(MUCb);
magb(l,3)=mean(MUCb);
end
%%}
% csvwrite('Brain_Temp_mean.txt',[beta',magb])
% csvwrite('Brain_Temp_var.txt',[beta',varb])