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function [marginal, msg, loglik] = smooth_evidence(engine, evidence)
[ss T] = size(evidence);
bnet = bnet_from_engine(engine);
onodes = engine.onodes;
hnodes = mysetdiff(1:ss, onodes);
hnodes = hnodes(:)';
ns = bnet.node_sizes(:);
onodes2 = [onodes(:); onodes(:)+ss];
ns(onodes2) = 1;
verbose = 0;
pot_type = 'd';
niter = engine.max_iter;
if verbose, fprintf('new smooth\n'); end
% msg(i1,t1,i2,j2) (i1,t1) -> (i2,t2)
%lambda_msg = cell(ss,T,ss,T);
%pi_msg = cell(ss,T,ss,T);
% intra_lambda_msg(i,j,t) (i,t) -> (j,t), i is child
% inter_lambda_msg(i,j,t) (i,t+1) -> (j,t), i is child
% inter_pi_msg(i,j,t) (i,t-1) -> (j,t), i is parent
intra_lambda_msg = cell(ss,ss,T);
inter_lambda_msg = cell(ss,ss,T);
inter_pi_msg = cell(ss,ss,T);
lambda = cell(ss,T);
pi = cell(ss,T);
for t=1:T
for i=1:ss
lambda{i,t} = ones(ns(i), 1);
pi{i,t} = ones(ns(i), 1);
cs = children(bnet.intra, i);
for c=cs(:)'
intra_lambda_msg{c,i,t} = ones(ns(i),1);
end
cs = children(bnet.inter, i);
for c=cs(:)'
inter_lambda_msg{c,i,t} = ones(ns(i),1);
end
ps = parents(bnet.inter, i);
for p=ps(:)'
inter_pi_msg{p,i,t} = ones(ns(i), 1); % not used for t==1
end
end
end
% each hidden node absorbs lambda from its observed child (if any)
for t=1:T
for i=hnodes
c = engine.obschild(i);
if c > 0
if t==1
fam = family(bnet.dag, c);
e = bnet.equiv_class(c, 1);
CPDpot = CPD_to_pot(pot_type, bnet.CPD{e}, fam, bnet.node_sizes(:), bnet.cnodes(:), evidence(:,1));
else
fam = family(bnet.dag, c, 2); % within 2 slice network
e = bnet.equiv_class(c, 2);
CPDpot = CPD_to_pot(pot_type, bnet.CPD{e}, fam, bnet.node_sizes(:), bnet.cnodes(:), evidence(:,t-1:t));
end
temp = pot_to_marginal(CPDpot);
lam_msg = normalise(temp.T);
intra_lambda_msg{c,i,t} = lam_msg;
end
end
end
for iter=1:engine.max_iter
% FORWARD
for t=1:T
% update pi
for i=hnodes
if t==1
e = bnet.equiv_class(i,1);
CPD = struct(bnet.CPD{e});
pi{i,t} = CPD.CPT;
else
e = bnet.equiv_class(i,2);
CPD = struct(bnet.CPD{e});
ps = parents(bnet.inter, i);
dom = [ps i+ss];
pot = dpot(dom, ns(dom), CPD.CPT);
for p=ps(:)'
temp = dpot(p, ns(p), inter_pi_msg{p,i,t});
pot = multiply_by_pot(pot, temp);
end
pot = marginalize_pot(pot, i+ss);
temp = pot_to_marginal(pot);
pi{i,t} = temp.T;
end
if verbose, fprintf('%d updates pi\n', i+(t-1)*ss); disp(pi{i,t}); end
end
% send pi msg to children
for i=hnodes
cs = children(bnet.inter, i);
for c=cs(:)'
pot = pi{i,t};
for k=cs(:)'
if k ~= c
pot = pot .* inter_lambda_msg{k,i,t};
end
end
cs2 = children(bnet.intra, i);
for k=cs2(:)'
pot = pot .* intra_lambda_msg{k,i,t};
end
inter_pi_msg{i,c,t+1} = normalise(pot);
if verbose, fprintf('%d sends pi to %d\n', i+(t-1)*ss, c+t*ss); disp(inter_pi_msg{i,c,t+1}); end
end
end
end
if verbose, fprintf('backwards\n'); end
% BACKWARD
for t=T:-1:1
% update lambda
for i=hnodes
pot = ones(ns(i), 1);
cs = children(bnet.inter, i);
for c=cs(:)'
pot = pot .* inter_lambda_msg{c,i,t};
end
cs = children(bnet.intra, i);
for c=cs(:)'
pot = pot .* intra_lambda_msg{c,i,t};
end
lambda{i,t} = normalise(pot);
if verbose, fprintf('%d computes lambda\n', i+(t-1)*ss); disp(lambda{i,t}); end
end
% send lambda msgs to hidden parents in prev slcie
for i=hnodes
ps = parents(bnet.inter, i);
if t > 1
e = bnet.equiv_class(i, 2);
CPD = struct(bnet.CPD{e});
fam = [ps i+ss];
for p=ps(:)'
pot = dpot(fam, ns(fam), CPD.CPT);
temp = dpot(i+ss, ns(i), lambda{i,t});
pot = multiply_by_pot(pot, temp);
for k=ps(:)'
if k ~= p
temp = dpot(k, ns(k), inter_pi_msg{k,i,t});
pot = multiply_by_pot(pot, temp);
end
end
pot = marginalize_pot(pot, p);
temp = pot_to_marginal(pot);
inter_lambda_msg{i,p,t-1} = normalise(temp.T);
if verbose, fprintf('%d sends lambda to %d\n', i+(t-1)*ss, p+(t-2)*ss); disp(inter_lambda_msg{i,p,t-1}); end
end
end
end
end
end
marginal = cell(ss,T);
for t=1:T
for i=hnodes
marginal{i,t} = normalise(pi{i,t} .* lambda{i,t});
end
end
loglik = 0;
msg.inter_pi_msg = inter_pi_msg;
msg.inter_lambda_msg = inter_lambda_msg;
msg.intra_lambda_msg = intra_lambda_msg;
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