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experiment_solar_rand.m
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experiment_solar_rand.m
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addpath(genpath('/homes/hkim/SSDGP/GPstuff-4.6'));
addpath(genpath('/Users/hyunjik11/Documents/SSDGP/GPstuff-4.6'));
time = 0;
num_workers=10;
POOL=parpool('local',num_workers);
warning('off','all');
%%% load and set up data %%%
load solar.mat
x=X; Y=y;
x_mean=mean(x); x_std=std(x);
y_mean=mean(y); y_std=std(y);
x = (x-x_mean)/x_std; %normalise x;
y = (y-y_mean)/y_std; %normalise y;
[n,D]=size(x);
%%%%%%%%%%%%%%%%%%%
numiter=10;
m_values=[10,20,40,80,160,320];
lm=length(m_values);
if time
gp_time = zeros(numiter,1);
var_time = zeros(numiter,lm);
nld_time = zeros(numiter,lm);
nip_time = zeros(numiter,lm);
parfor iter = 1:numiter
warning('off','all');
for ind=1:lm
m = m_values(ind);
%fprintf('m=%d \n',m);
%parfor i=1:10
%t=getCurrentTask(); k=t.ID;
%filename=['experiment_results/mauna10m',num2str(k),'.txt'];
%fileID=fopen(filename,'at');
%%% Initialise gp_var %%%
lik=lik_init(y);
gpcf_se1=se_init(x,y);
gpcf_se2=se_init(x,y);
gpcf_se=gpcf_sum('cf',{gpcf_se1,gpcf_se2});
gpcf_per = per_init(x,y);
gpcf=gpcf_prod('cf',{gpcf_se,gpcf_per});
opt=optimset('TolFun',1e-4,'TolX',1e-5,'Display','off','MaxIter',1000);
%%% Optimise gp %%%
if m==min(m_values)
gp = gp_set('lik',lik,'cf',gpcf);
tic;
gp = gp_optim(gp,x,y,'opt',opt,'optimf',@fminscg);
time = toc;
gp_time(iter)=time;
end
%%% Optimise gp_var %%%
if subset
X_u = datasample(x,m,1,'Replace',false);
else
[~,X_u]=kmeans(x,m); %inducing pts initialised by Kmeans++
end
gp_var = gp_set('type', 'VAR', 'lik', lik, 'cf',gpcf,'X_u', X_u);
gp_var = gp_set(gp_var, 'infer_params', 'covariance+likelihood');
tic;
gp_var=gp_optim(gp_var,x,y,'opt',opt,'optimf',@fminscg);
time=toc;
var_time(iter,ind) = time;
%fprintf('Time taken for optimising VAR: %4.2f s \n',time);
energy=gp_e([],gp_var,x,y);
signal_var=gp_var.lik.sigma2;
%%% Extract inducing points from VAR %%%
xu=gp_var.X_u;
%%% Compute UB to NLD %%%
tic;
K_mn=gp_cov(gp_var,xu,x); K_mm=gp_trcov(gp_var,xu);
L_mm=chol(K_mm); %L_mm'*L_mm=K_mm;
L=L_mm'\K_mn; %L'*L=K_hat=K_mn'*(K_mm\K_mn)
A=L*L'+signal_var*eye(m);
L_naive=chol(A);
time=toc;
%fprintf('Time taken for computing L_naive: %4.4f s \n',time);
nld_time(iter,ind) = time;
naive_nld=(m-n)*log(signal_var)/2-sum(log(diag(L_naive)));
K_naive=L'*L;
%%% Compute RFF and use as UB to NLD %%%
l1=gp_var.cf{1}.cf{1}.cf{1}.lengthScale; sf1=gp_var.cf{1}.cf{1}.cf{1}.magnSigma2;
l2=gp_var.cf{1}.cf{1}.cf{2}.lengthScale; sf2=gp_var.cf{1}.cf{1}.cf{2}.magnSigma2;
lper=gp_var.cf{1}.cf{2}.lengthScale; sfper=gp_var.cf{1}.cf{2}.magnSigma2;
per=gp_var.cf{1}.cf{2}.period;
tic;
phi=solarRFF(x,m,l1,sf1,l2,sf2,lper,per,sfper);
Ar=phi*phi'+signal_var*eye(m);
L_rff=chol(Ar);
time=toc;
%fprintf('Time taken for computing L_rff: %4.4f s \n',time);
rff_nld=(m-n)*log(signal_var)/2-sum(log(diag(L_rff)));
%%% Compute UB to NIP %%%
[K,C]=gp_trcov(gp_var,x);
tic;
[~,~,~,~,cg_resvec,cg_obj]=cgs_obj(C,y,[],m);
time=toc;
%fprintf('Time taken for CG: %4.4f s \n',time);
K_fic=K_naive+diag(diag(K)-diag(K_naive));
dinv=1./(diag(K)-diag(K_naive)+signal_var);
Dinv=diag(dinv); %D=diag(K-K_naive)+signal_var*eye(n)
Af=L*Dinv*L'+eye(m);
%function handle which gives (K_naive+signal_var*eye(n))\x
myfun = @(w) (w-L'*(A\(L*w)))/signal_var;
%function handle which gives (K_fic+signal_var*eye(n))\x
myfunf = @(w) (w-L'*(Af\(L*(w.*dinv)))).*dinv;
%funcion handle which gives (K_pic+signal_var*eye(n))\x
[Kb,invfun]=blockdiag(K-K_naive,m,signal_var); %invfun is fhandle which gives (Kb+signal_var*eye(n))\w
K_pic=K_naive+Kb;
%fprintf('Time taken for Ap: %4.4f s \n',time1);
tic; [~,~,~,~,pcg_resvec,pcg_obj]=cgs_obj(C,y,[],m,myfun); time=toc;
%fprintf('Time taken for PCG Nystrom: %4.4f s \n',time);
tic; [~,~,~,~,pcg_resvecf,pcg_objf]=cgs_obj(C,y,[],m,myfunf); time=toc;
%fprintf('Time taken for PCG FIC: %4.4f s \n',time);
tic;
Ap=L*invfun(L')+eye(m);
myfunp = @(w) invfun(w-L'*(Ap\(L*invfun(w))));
[~,~,~,~,pcg_resvecp,pcg_objp]=cgs_obj(C,y,[],m,myfunp); time=toc;
nip_time(iter,ind) = time;
%fprintf('Time taken for PCG PIC: %4.4f s \n',time);
cg_obj=minsofar(cg_obj);
pcg_obj=minsofar(pcg_obj);
pcg_objf=minsofar(pcg_objf);
pcg_objp=minsofar(pcg_objp);
%fprintf('worker %d done \n',i);
%end
end
end
else
lb_table=zeros(numiter,lm);
naive_nld_table=zeros(1,lm);
rff_nld_table=zeros(numiter,lm);
cg_obj_table=zeros(1,lm);
pcg_obj_table=zeros(1,lm);
pcg_objf_table=zeros(1,lm);
pcg_objp_table=zeros(1,lm);
nld = zeros(1,lm);
nip = zeros(1,lm);
ne = zeros(1,lm);
ne_full = zeros(numiter,1);
gp_var_cell=cell(1,10);
idx_u=1:n;
gp_var_opt = 0;
for ind = 1:lm
m=m_values(ind);
fprintf('m=%d \n',m);
parfor i=1:numiter
rng(i);
warning('off','all');
%t=getCurrentTask(); k=t.ID;
%filename=['experiment_results/mauna10m',num2str(k),'.txt'];
%fileID=fopen(filename,'at');
%%% Initialise gp_var %%%
if m == min(m_values) || i < numiter
lik=lik_init(y);
gpcf_se1=se_init(x,y);
gpcf_se2=se_init(x,y);
gpcf_se=gpcf_sum('cf',{gpcf_se1,gpcf_se2});
gpcf_per = per_init(x,y);
gpcf=gpcf_prod('cf',{gpcf_se,gpcf_per});
else
lik = gp_var_opt.lik;
gpcf = gp_var_opt.cf;
end
%%% Optimise gp %%%
if m==min(m_values)
gp = gp_set('lik',lik,'cf',gpcf);
gp = gp_optim(gp,x,y,'opt',opt,'optimf',@fminscg);
ne_full(i) = gp_e([],gp,x,y);
end
%%% Optimise gp_var %%%
if i <= numiter/2
[X_u, idx_cell{i}] = datasample(x,m,1,'Replace',false);
else
weights = 1e-10*ones(1,n); %weights for sampling
weights(idx_u)=1; %make sure samples idx_u are included
[X_u,idx_cell{i}] = datasample(x,m,1,'Replace',false,'Weights',weights);
end
gp_var = gp_set('type', 'VAR', 'lik', lik, 'cf',gpcf,'X_u', X_u);
gp_var = gp_set(gp_var, 'infer_params', 'covariance+likelihood');
opt=optimset('TolFun',1e-4,'TolX',1e-5,'Display','off','MaxIter',1000);
gp_var=gp_optim(gp_var,x,y,'opt',opt,'optimf',@fminscg);
energy=gp_e([],gp_var,x,y);
%%% Record ml and gp_var %%%
lb_table(i,ind)=-energy;
gp_var_cell{i} = gp_var;
%fprintf('optim for worker %d done \n',i);
end
%%% Get index of best var LB %%%
[~,maxind]=max(lb_table(:,ind));
gp_var = gp_var_cell{maxind};
gp_var_opt = gp_var;
%%% Compute ne of full GP for these hyp %%%
gp = gp_set('lik',gp_var.lik,'cf',gp_var.cf);
energy = gp_e([],gp,x,y);
ne(ind) = -energy;
%%% Extract inducing points and signal_var from VAR %%%
idx_u = idx_cell{maxind};
xu=gp_var.X_u;
signal_var=gp_var.lik.sigma2;
%%% Compute UB to NLD %%%
K_mn=gp_cov(gp_var,xu,x); K_mm=gp_trcov(gp_var,xu);
L_mm=chol(K_mm); %L_mm'*L_mm=K_mm;
L=L_mm'\K_mn; %L'*L=K_hat=K_mn'*(K_mm\K_mn)
A=L*L'+signal_var*eye(m);
L_naive=chol(A);
naive_nld=(m-n)*log(signal_var)/2-sum(log(diag(L_naive)));
K_naive=L'*L;
[K,C]=gp_trcov(gp_var,x);
%%% Compute true nld, nip and hence ml with hyp in var_gp %%%
Ltemp = chol(C); ztemp = Ltemp'\y ;
nld(ind) = -sum(log(diag(Ltemp)));
nip(ind) = -sum(ztemp.^2)/2;
%%% Compute UB to NIP %%%
[~,~,~,~,cg_resvec,cg_obj]=cgs_obj(C,y,[],m);
K_fic=K_naive+diag(diag(K)-diag(K_naive));
dinv=1./(diag(K)-diag(K_naive)+signal_var);
Dinv=diag(dinv); %D=diag(K-K_naive)+signal_var*eye(n)
Af=L*Dinv*L'+eye(m);
%function handle which gives (K_naive+signal_var*eye(n))\x
myfun = @(w) (w-L'*(A\(L*w)))/signal_var;
%function handle which gives (K_fic+signal_var*eye(n))\x
myfunf = @(w) (w-L'*(Af\(L*(w.*dinv)))).*dinv;
%funcion handle which gives (K_pic+signal_var*eye(n))\x
[Kb,invfun]=blockdiag(K-K_naive,m,signal_var); %invfun is fhandle which gives (Kb+signal_var*eye(n))\w
K_pic=K_naive+Kb;
Ap=L*invfun(L')+eye(m);
myfunp = @(w) invfun(w-L'*(Ap\(L*invfun(w))));
[~,~,~,~,pcg_resvec,pcg_obj]=cgs_obj(C,y,[],m,myfun);
[~,~,~,~,pcg_resvecf,pcg_objf]=cgs_obj(C,y,[],m,myfunf);
[~,~,~,~,pcg_resvecp,pcg_objp]=cgs_obj(C,y,[],m,myfunp);
cg_obj=minsofar(cg_obj);
pcg_obj=minsofar(pcg_obj);
pcg_objf=minsofar(pcg_objf);
pcg_objp=minsofar(pcg_objp);
%gather all results
cg_obj_table(ind)=cg_obj(end);
pcg_obj_table(ind)=pcg_obj(end);
pcg_objf_table(ind)=pcg_objf(end);
pcg_objp_table(ind)=pcg_objp(end);
naive_nld_table(ind)=naive_nld;
%%% Compute RFF and use as UB to NLD %%%
l1=gp_var.cf{1}.cf{1}.cf{1}.lengthScale; sf1=gp_var.cf{1}.cf{1}.cf{1}.magnSigma2;
l2=gp_var.cf{1}.cf{1}.cf{2}.lengthScale; sf2=gp_var.cf{1}.cf{1}.cf{2}.magnSigma2;
lper=gp_var.cf{1}.cf{2}.lengthScale; sfper=gp_var.cf{1}.cf{2}.magnSigma2;
per=gp_var.cf{1}.cf{2}.period;
parfor j=1:numiter
rng(j);
phi=solarRFF(x,m,l1,sf1,l2,sf2,lper,per,sfper);
Ar=phi*phi'+signal_var*eye(m);
L_rff=chol(Ar);
rff_nld=(m-n)*log(signal_var)/2-sum(log(diag(L_rff)));
rff_nld_table(i,ind)=rff_nld;
%fprintf('RFF for worker %d done \n',i);
end
% fprintf('ml=%4.3f \n',nld(ind)+nip(ind)-n*log(2*pi)/2);
% fprintf('PER magnSigma2=%4.3f, period=%4.3f \n',...
% gp_var.cf{1}.cf{2}.magnSigma2, gp_var.cf{1}.cf{2}.period);
% fprintf('SE1 magnSigma2=%4.3f, l=%4.3f \n',...
% gp_var.cf{1}.cf{1}.cf{1}.magnSigma2, gp_var.cf{1}.cf{1}.cf{1}.lengthScale);
% fprintf('SE2 magnSigma2=%4.3f, l=%4.3f \n',...
% gp_var.cf{1}.cf{1}.cf{2}.magnSigma2, gp_var.cf{1}.cf{1}.cf{2}.lengthScale);
% fprintf('lik sigma2=%4.8f \n',gp_var.lik.sigma2);
end
end
delete(POOL)