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function bnet_miss = gener_MAR_net(bnet_orig, base_proba)
% function bnet_miss = gener_MAR_net(bnet_orig, base_proba)
%
% bnet_orig : a bnet
% base_proba : a probability for value to be missing
%
% bnet_miss : a bnet that could be used in gener_data_from_bnet_miss function
% to generate incomplete MAR dataset
%
% Francois.Olivier.C.H@gmail.com
%%%%%%%%%%%% INIT
if nargin<2, error('Not enougth arguments'); end
% création du réseau
dag = bnet_orig.dag;
N = size(dag,2);
ns = bnet_orig.node_sizes;
ns_miss = zeros(1,3*N);
ns_miss(1:N) = ns;
ns_miss(N+1:2*N) = 2*ones(1,N); % 1= node i-N present, 2= node i-N missing
ns_miss(2*N+1:3*N) = ns+1; % 1:ns, absent
dag_miss = zeros(3*N,3*N);
dag_miss(1:N,1:N) = dag;
% dag_miss(2*N+1:3*N,N+1:2*N)=mk_rnd_dag(N,N-ceil(rand*N/2));
lim = 1+(rand>.4)+(rand>.65)+(rand>.9);
dag_miss(2*N+1:3*N,N+1:2*N)=mk_rnd_dag(N,lim);
for i=1:N, dag_miss(i,2*N+i)=1; dag_miss(N+i,2*N+i)=1; dag_miss(2*N+i,i)=0; dag_miss(2*N+i,N+i)=0; end
bnet_miss = mk_bnet(dag_miss, ns_miss);
CPT = CPT_from_bnet(bnet_orig, 0);
for i=1:N
bnet_miss.CPD{i} = tabular_CPD (bnet_miss, i, CPT{i});
end
% CPD of nodes M
for i=1:N,
if find(bnet_miss.order==i)<find(bnet_miss.order==N+i),
CPT_M=[];
for j=1:ns_miss(i), for l=1:ns_miss(N+i), for k=1:ns_miss(2*N+i),
CPT_M=[CPT_M (((j==k)&(l==1))|((k==ns_miss(2*N+i))&(l==2)))];
end, end, end
else
CPT_M=[];
for k=1:ns_miss(2*N+i), for l=1:ns_miss(N+i), for j=1:ns_miss(i),
CPT_M=[CPT_M (((j==k)&(l==1))|((k==ns_miss(2*N+i))&(l==2)))];
end, end, end
end
bnet_miss.CPD{2*N+i} = tabular_CPD (bnet_miss, 2*N+i, CPT_M);
end
%%%%%%%%%%%% Base probability of missing value
p = base_proba;
for i=1:N
fam = find(dag_miss(:,N+i)==1)';
semisize = prod(ns_miss(fam)); % as node N+i is binary to say i is present or missing
CPT = zeros(1,2*semisize);
CPT(1:semisize) = 1-p;
CPT(semisize+1:2*semisize) = p;
bnet_miss.CPD{N+i} = tabular_CPD (bnet_miss, N+i, CPT);
end
BETA = gener_discrete_dist(N, base_proba);
order=[];
missdagtmp = bnet_miss.dag; %(N+1:2*N,N+1:2*N);
unprocessed = 1:N;
while ~isempty(unprocessed)
npar=[];
for i=N+1:2*N, npar(end+1)=length(parents(missdagtmp,i));end, % to be verifie from here
[npar, ord] = sort(npar);
while ~ismember(ord(1),unprocessed)
ord=ord(2:end);
end
order = [order, ord(1)];
missdagtmp(ord(1),:)=0;
unprocessed = mysetdiff(unprocessed,ord(1));
end
%%%%%%%%%%%% Update CPT with MCAR process
for i=1:length(BETA)
fam_miss = find(dag_miss(:,N+order(i))==1)';
p=BETA(i);
semisize = prod(ns_miss(fam_miss));
if isempty(fam_miss),
CPT = zeros(1,2*semisize);
CPT(1:semisize) = 1-p;
CPT(semisize+1:2*semisize) = p;
bnet_miss.CPD{N+order(i)} = tabular_CPD (bnet_miss, N+order(i), CPT);
else
MUi1k = gener_discrete_dist(semisize, p);
CPT = zeros(1,2*semisize);
CPT(1:semisize) = 1-MUi1k;
CPT(semisize+1:2*semisize) = MUi1k;
bnet_miss.CPD{N+order(i)} = tabular_CPD (bnet_miss, N+order(i), CPT);
end
end
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