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function [bnet0, Sbest, Obest] = learn_struct_mwst_EM(data, discrete, node_sizes, prior, nbloopmax, thresh)
% LEARN_STRUCT_MWST_EM Learn an oriented tree using the MSWT algorithm
% [bnet, Ebic] = learn_struct_mwstem(data, discrete, node_sizes, prior,
% nbloopmax, thresh)
%
% Input :
% data{i,m} a cell where the node i in the case m,
% discrete = [ 1 if discret-node 0 if not ], (1:N)
% node_sizes = 1 if gaussian node, (max on complete samples)
% prior = 1 to use uniform Dirichlet prior (0)
% nbloopmax = max loop number (ceil(log(N*log(N))))
% thresh = the convergence test's threshold (1e-3)
%
% Output :
% bnet = the output bayesian network
% Ebic = the espected BIC score of bnet given the data
%
% francois.olivier.c.h@gmail.com
%%%%%%%%%%%%%
%fprintf('-- INITIALIZATION\n');
%%%%%%%%%%%%%
[N, m]=size(data);
rand('state',sum(100*clock))
if nargin<6, thresh = 1e-4; end
if nargin<5, nbloopmax = 15; end
if nargin<4, prior = 0; end
if nargin<3,
misv = -9999;
data_mat = bnt_to_mat(data,misv);
node_sizes = max(data_mat'),
end
if nargin<2, discrete = ones(1,N); end
nbloop = 1; last=0;
max_iter = 6; % for learn_struct_params
%%%%%%%%%%%%%
%fprintf(' Choice of the first bnet ');tic
%%%%%%%%%%%%%
% Random Chain like DAG
T = diag(ones(N-1,1),1); T=T+T';
order=randperm(N); root=randperm(N); root=root(1);
[tmp order2]=sort(order); order2;
T2 = full(mk_rooted_tree(T,order2(root)));
torder=topological_sort(T2(order2,order2));
[tmp torder2]=sort(torder); torder2;
ordre = 1:N;torder=ordre;torder2=ordre;order2=ordre;
%figure(2), subplot(3,2,1), draw_graph(T2(order2,order2));drawnow
bnet0 = mk_bnet(T2(order2(torder),order2(torder)), node_sizes(torder));
%for i=1:N, bnet0.CPD{i} = tabular_CPD(bnet0, i); end % probleme de log of zeros si tous les cas ne sont pas repr�sent�s dans la base
for i=1:N, bnet0.CPD{i} = tabular_CPD(bnet0, i, 'prior_type', 'dirichlet', 'dirichlet_type', 'unif'); end % a priori -> change les espected counts
%tmp = toc;fprintf(' : %6.2f seconds\n',tmp);
Sbest = -Inf; Bbest = bnet0; fini=0;T3=T2;
while not(fini)
%%%%%%%%%%%%%
%fprintf('Loop %d : learning parameters...\n',nbloop);tic
% engine0=jtree_sparse_inf_engine(bnet0);
engine0=jtree_inf_engine(bnet0);
[bnet1, LL1, engine1] = learn_params_em(engine0, data(torder,:), max_iter, thresh);
%tmp = toc;
%fprintf(' Parameters learning : %6.2f seconds\n',tmp);
BIC0=0;
for i=1:N,
xxx=struct(bnet1.CPD{i});
BIC0=BIC0+bic_score_family(xxx.counts, xxx.CPT, xxx.nsamples);
end
%fprintf('%d ',torder), fprintf('%5.2f\n',BIC0);
%figure(2), subplot(3,2,nbloop), title(sprintf('%5.2f',BIC0));
if BIC0 < Sbest+ thresh*abs(Sbest) | nbloop>nbloopmax
fini=1;
else
Sbest = BIC0;
Bbest = bnet1;
Obest = torder2 ;
Tbest = T3;
%%%%%%%%%%%%%
%tic;
%%%%%%%%%%%%%
theta_Xi=cell(N,1);
evidence = cell(1,N);
[engine2, loglik] = enter_evidence(engine1, evidence);
for j=1:N,
SS= marginal_nodes (engine2,torder2(j));
theta_Xi{j} = SS.T;
end
theta_Xj_given_Xi = cell(N,N);
for i=1:N
for vali = 1:node_sizes(i)
evidence = cell(1,N); evidence{torder2(i)} = vali;
[engine2, loglik] = enter_evidence(engine1, evidence);
for j=mysetdiff(1:N,i)
SS= marginal_nodes (engine2,torder2(j));
theta_Xj_given_Xi{j,i} = [theta_Xj_given_Xi{j,i}, SS.T];
end
end
end
%celldisp(theta_Xi);
BIC_mat=zeros(N,N);
for i=1:N,
BIC_mat(i,i)=bic_score_family(theta_Xi{i}*m,theta_Xi{i},m);
for j=mysetdiff(1:N,i)
theta_XjXi=(ones(node_sizes(i),1)*theta_Xi{j}').*theta_Xj_given_Xi{i,j};
BIC_mat(i,j)= bic_score_family(m*theta_XjXi,theta_Xj_given_Xi{i,j},m);
end
end
BIC_delta = BIC_mat-diag(BIC_mat)*ones(1,N);
BIC1=0;
for i = 1:N
j = find(bnet0.dag(:,i)==1);
if isempty(j)
BIC1 = BIC1 + BIC_mat(torder2(i),torder2(i));
else
BIC1 = BIC1 + BIC_mat(torder2(i),torder2(j));
end
end
%fprintf('%d ',torder), fprintf('%5.2f (1)\n',BIC1);
%fprintf(' Creation of the score matrix ');
%tmp = toc;fprintf(' : %6.2f seconds\n',tmp);
%%%%%%%%%%%%%
%fprintf(' Creation of the new bnet ');tic
%%%%%%%%%%%%%
T2 = minimum_spanning_tree(-BIC_delta);
root=randperm(N); root=root(1);
T3 = full(mk_rooted_tree(T2, root));
torder=topological_sort(T3);
[tmp torder2]=sort(torder); torder2;
bnet0 = mk_bnet(T3(torder,torder), node_sizes(torder));
%bnet0.order
%BIC=0;
for i = 1:N
j = find(T3(:,i)==1);
if isempty(j)
bnet0.CPD{torder2(i)} = tabular_CPD(bnet0, torder2(i), 'CPT', theta_Xi{i}, 'prior_type', 'dirichlet', 'dirichlet_type', 'unif');
%BIC = BIC + BIC_mat(i,i);
else
bnet0.CPD{torder2(i)} = tabular_CPD(bnet0, torder2(i), 'CPT', theta_Xj_given_Xi{i,j}, 'prior_type', 'dirichlet', 'dirichlet_type', 'unif');
%BIC=BIC + BIC_mat(i,j);
end
end
nbloop=nbloop+1;
%figure(2), subplot(3,2,nbloop), draw_graph(T3); drawnow
%tmp = toc;fprintf(' : %6.2f seconds\n',tmp);
fprintf('================================================================================\n');
%fprintf(' --> BIC score = %6.2f\n\n\n',BIC);
theta_Xi_best=theta_Xi;
theta_Xj_given_Xi_best=theta_Xj_given_Xi;
end
end
% Bbest.dag
% Tbest
% bnet = mk_bnet(Tbest, node_sizes);
% for i=1:N, bnet.CPD{i} = tabular_CPD(bnet, i, 'prior_type', 'dirichlet', 'dirichlet_type', 'unif'); end
% engine=jtree_sparse_inf_engine(bnet);
% [Bbest, LL1] = learn_params_em(engine, data, max_iter, thresh);
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