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SMC_Static_Affy.m
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SMC_Static_Affy.m
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clear all; close all; clc;
% rng('default');
% rng(1000000); %1000
tic;
load('Affy_2cells_Data');
Affy_2cells_Data = double(Affy_2cells_Data);
pu1 = Affy_2cells_Data(:,31:33); sum_pu1 = sum(pu1'); avg_pu1 = sum_pu1'/3;
pu2 = Affy_2cells_Data(:,1:3); sum_pu2 = sum(pu2'); avg_pu2 = sum_pu2'/3;
cell_spec_expr_value = [avg_pu1 avg_pu2];
%%% SAMPLES FOR THOROUGH ANALYSIS
YY1 = Affy_2cells_Data(:,10:12);
YY2 = Affy_2cells_Data(:,22:24);
%YY = [YY1 YY2]; % CONTAINS 6 SAMPLES FOR ANALYSIS
YY = Affy_2cells_Data(:,4:30);
%cell_prop = [0.25 0.25 0.25 0.75 0.75 0.75;...
%0.75 0.75 0.75 0.25 0.25 0.25];
cell_prop = [0.05 0.05 0.05 0.10 0.10 0.10 0.25 0.25 0.25 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.75 0.75 0.75 0.90 0.90 0.90 0.95 0.95 0.95 ;...
0.95 0.95 0.95 0.90 0.90 0.90 0.75 0.75 0.75 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.25 0.25 0.25 0.10 0.10 0.10 0.05 0.05 0.05];
ibere = 5000;
M = cell_prop;
X = cell_spec_expr_value(ibere:end,:);
Y = YY(ibere:end,:);
% Y1 = X*M;
% errorr = (Y - Y1);
% err_vec = errorr(:);
% mean_ML = mean(err_vec);
% varr_global = mean((err_vec - mean_ML).^2);
I = size(Y,1);
J = size(Y,2);
K = size(M,1);
n_para = I*K + K*J + 1;
% ch1 = 0.0001 ;
% ch2 = 0.0001;
% mid = 0.8;
%
% E_r1 = 0:ch1:mid-ch1;
% E_r2 = mid:ch2:1;
% E_r = [E_r1 E_r2];
%
% T = length(E_r);
E_r = 0:0.0002:1;
T = length(E_r);
N = 40; % 10
%%% PRIOR SPEC
% 1. M
mA = 0.5; sdM = 0.1; vA = sdM^2;
M_bar = mA*ones(K,J);
M_bar_VEC = M_bar(:);
var_MM = vA*ones(K,J);
var_MM_VEC = var_MM(:);
% 2. precision
alpha_prior = 2;
beta_prior = 100000; %100000
% 3. X
%
% M_X = [0.4 0.4 0.6 0.6 0.7 0.6;...
% 0.6 0.6 0.4 0.4 0.3 0.4];
% M_X = [M_X];
%
% for i = 1:I
% yy = Y(i,:)';
% DD = M_X';
%
% xx = lsqnonneg(DD,yy);
% X_priors(i,:) = xx';
%
%
% end
X_priors = 30*ones(I,K);
var_pri_X = 1000;
vv = 1/var_pri_X;
X_priors_tran = X_priors';
X_priors_VECTOR = X_priors_tran(:);
clear X_priors_tran;
wt_all = zeros(T,N);
theta_all = zeros(n_para,N);
%%% KERNEL
%ksdM = 0.0001;
%ksdX = 0.2;
for t = 1:T
t
T
theta = zeros(n_para,N);
if t == 1
%1. Sample M
for kj = 1:K*J
meM = M_bar_VEC(kj);
va_M = var_MM_VEC(kj);
samM = normrnd(meM,sqrt(va_M),[1,N]);
theta(kj,:) = samM;
% beM = K*(j-1) + 1;
% enM = K*j;
end
%2. Sample lambda i.e precision
theta(K*J + 1,:) = gamrnd(alpha_prior,1/beta_prior,[1 N]);
%3. Sample lambda i.e precision
for ik = 1:I*K
meX = X_priors_VECTOR(ik);
sdX = sqrt(var_pri_X);
samX = normrnd(meX,sdX,[1,N]);
theta(K*J + 1+ ik,:) = samX;
%theta(K*J + I + ik,:) = samX;
end
wt = (1/N)*ones(1,N);
else % t = 2,...T
EE = (E_r(t) - E_r(t-1));
theta_prev = theta_all;
wt_prev = wt_all(t-1,:);
%%% COMPUTATION OF WEIGHTS
%pdf_lik = zeros(1,N);
for n = 1:N
prev_par = theta_prev(:,n);
MM_vec = prev_par(1:K*J);
MM_mat = vec2mat(MM_vec,K)';
PREC = prev_par(1 + K*J);
XX_vec = prev_par(2 + K*J:end);
%XX_vec = prev_par(1 + K*J + I:end);
XX_mat = vec2mat(XX_vec,K);
MEAN_Y = XX_mat*MM_mat;
err_sq = (Y - MEAN_Y).^2;
exp_n = -0.5*EE*(PREC)*sum(sum(err_sq));
pdfY = (PREC^(vpa(I*J*0.5*EE)))*exp(vpa(exp_n));
pdf_lik(n) = pdfY;
end
wt_int = wt_prev.*pdf_lik;
clear pdf_lik;
wt = wt_int/sum(wt_int);
wt = double(wt);
%%% resampling step
neff = 1/sum(wt.^2);
if neff<N/10
rr = randsample([1:N],N,true,wt);
theta_prev = theta_prev(:,rr);
wt = (1/N)*ones(1,N);
end
%%% MUTATION
for n = 1:N
thet_lana = theta_prev(:,n);
thet_lana_M = thet_lana(1:K*J);
thet_lana_M_mat = vec2mat(thet_lana_M,K)';
M_M1 = thet_lana_M_mat;
PRECIS = thet_lana(1 + K*J);
thet_lana_X = thet_lana(2+K*J:end);
thet_lana_X_mat = vec2mat(thet_lana_X,K);
%%% move PRECISION
alp_p = alpha_prior + (I*J*E_r(t))/2;
beta_p = beta_prior + E_r(t)*0.5*sum(sum((Y - thet_lana_X_mat*thet_lana_M_mat).^2));
new_prec = gamrnd(alp_p,1/beta_p);
E_var = E_r(t)*new_prec;
%%% move the M's
for k = 1:K
for j = 1:J
meaM = M_bar(k,j);
var_M = var_MM(k,j);
X_k = thet_lana_X_mat(:,k);
Y_j = Y(:,j);
u1 = (1/var_M);
u2 = E_var*sum(X_k.^2);
U_kj = u1 + u2;
v1 = E_var*sum(Y_j.*X_k);
X_del = thet_lana_X_mat;
X_del(:,k) = 0;
mmj = M_M1(:,j);
Bijk = X_del*mmj;
v2 = E_var*sum(X_k.*Bijk);
v3 = meaM/var_M;
V_kj = v1 - v2 + v3;
meNN = V_kj/U_kj;
varNN = 1/U_kj;
samNN = normrnd(meNN,sqrt(varNN));
M_M1(k,j) = samNN;
end
end
%%% MOVE the X's
M_here = M_M1;
for i = 1:I
for k = 1:K
mu_ik = X_priors(i,k);
M_k = M_here(k,:);
Y_i = Y(i,:);
%%% Q_ik
u1 = vv;
sum_mj_sqr = sum(M_k.^2);
u2 = E_var*sum_mj_sqr;
Q_ik = u1 + u2;
%%% P_ik
BB1 = E_var*sum(M_k.*Y_i);
X_i = thet_lana_X_mat(i,:);
X_i(k) = 0;
X_i_minus = X_i;
Y_minus = X_i_minus*M_here;
BB2 = E_var*sum(M_k.*Y_minus);
BB3 = vv*mu_ik;
P_ik = BB1 - BB2 + BB3;
mea_x_ik = P_ik/Q_ik;
var_x_ik = 1/Q_ik;
sam_x_ik = normrnd(mea_x_ik,sqrt(var_x_ik));
thet_lana_X_mat(i,k) = sam_x_ik;
end
end
XXMM = thet_lana_X_mat';
theta(:,n) = [M_here(:); new_prec; XXMM(:)];
clear XXMM;
end
end
wt_all(t,:) = wt;
theta_all = theta;
end
%%% M part
M_part = theta(1:K*J,:);
MB = M_part.*repmat(wt,K*J,1);
mean_M = sum(MB')';
M_est1 = vec2mat(mean_M,K)';
M_est = M_est1./repmat(sum(M_est1),K,1)
%%% prec part
prec_part = theta(1+K*J,:);
ghh = sum(prec_part.*wt);
var_est = 1/ghh
%%% X part
X_part = theta(2+K*J:end,:);
XB = X_part.*repmat(wt,I*K,1);
mean_X = sum(XB')';
X_est = vec2mat(mean_X,K);
cor1 = corr2(X(:,1),X_est(:,1));
cor2 = corr2(X(:,1),X_est(:,2));
if cor1 > cor2
corr_M = corr2(M(:),M_est(:))
else
corr_M = -corr2(M(:),M_est(:))
end
time = toc