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function [marginal, msg, loglik] = smooth_evidence(engine, evidence)
% [marginal, msg, loglik] = smooth_evidence(engine, evidence) (pearl_dbn)
disp('warning: pearl_dbn smoothing is broken');
[ss T] = size(evidence);
bnet = bnet_from_engine(engine);
bnet2 = dbn_to_bnet(bnet, T);
ns = bnet2.node_sizes;
hnodes = mysetdiff(1:ss, engine.onodes);
hnodes = hnodes(:)';
onodes2 = unroll_set(engine.onodes(:), ss, T);
onodes2 = onodes2(:)';
hnodes2 = unroll_set(hnodes(:), ss, T);
hnodes2 = hnodes2(:)';
[engine.parent_index, engine.child_index] = mk_pearl_msg_indices(bnet2);
msg = init_msgs(bnet2.dag, ns, evidence, bnet2.equiv_class, bnet2.CPD);
verbose = 0;
pot_type = 'd';
niter = 1;
for iter=1:niter
% FORWARD
for t=1:T
if verbose, fprintf('t=%d\n', t); end
% each hidden node absorbs lambda from its observed child (if any)
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, 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);
n = i + (t-1)*ss;
lam_msg = normalise(temp.T);
j = engine.child_index{n}(c+(t-1)*ss);
assert(j==1);
msg{n}.lambda_from_child{j} = lam_msg;
if verbose, fprintf('%d sends lambda to %d\n', c + (t-1)*ss, n); disp(lam_msg); end
end
end
% update pi
for i=hnodes
n = i + (t-1)*ss;
ps = parents(bnet2.dag, n);
if t==1
e = bnet.equiv_class(i,1);
else
e = bnet.equiv_class(i,2);
end
msg{n}.pi = compute_pi(bnet.CPD{e}, n, ps, msg);
if verbose, fprintf('%d computes pi\n', n); disp(msg{n}.pi); end
end
% send pi msg to children in next slice
for i=hnodes
n = i + (t-1)*ss;
%cs = myintersect(children(bnet2.dag, n), hnodes2);
cs = children(bnet2.dag, n);
for c=cs(:)'
j = engine.parent_index{c}(n); % n is c's j'th parent
pi_msg = normalise(compute_pi_msg(n, cs, msg, c, ns));
msg{c}.pi_from_parent{j} = pi_msg;
if verbose, fprintf('%d sends pi to %d\n', n, c); disp(pi_msg); end
end
end
end
% BACKWARD
for t=T:-1:1
if verbose, fprintf('t = %d\n', t); end
% update lambda
for i=hnodes
n = i + (t-1)*ss;
cs = children(bnet2.dag, n);
msg{n}.lambda = compute_lambda(n, cs, msg, ns);
if verbose, fprintf('%d computes lambda\n', n); disp(msg{n}.lambda); end
end
% send lambda msgs to hidden parents in prev slcie
for i=hnodes
n = i + (t-1)*ss;
%ps = myintersect(parents(bnet2.dag, n), hnodes2);
ps = parents(bnet2.dag, n);
for p=ps(:)'
j = engine.child_index{p}(n); % n is p's j'th child
if t > 1
e = bnet.equiv_class(i, 2);
else
e = bnet.equiv_class(i, 1);
end
lam_msg = normalise(compute_lambda_msg(bnet.CPD{e}, n, ps, msg, p));
msg{p}.lambda_from_child{j} = lam_msg;
if verbose, fprintf('%d sends lambda to %d\n', n, p); disp(lam_msg); end
end
end
% send pi msg to observed children
if 0
for i=hnodes
n = i + (t-1)*ss;
cs = myintersect(children(bnet2.dag, n), onodes2);
%cs = children(bnet2.dag, n);
for c=cs(:)'
j = engine.parent_index{c}(n); % n is c's j'th parent
pi_msg = normalise(compute_pi_msg(n, cs, msg, c, ns));
msg{c}.pi_from_parent{j} = pi_msg;
if verbose, fprintf('%d sends pi to %d\n', n, c); disp(pi_msg); end
end
end
end
end
end
marginal = cell(ss,T);
lik = zeros(1,ss*T);
for t=1:T
for i=hnodes
n = i + (t-1)*ss;
[bel, lik(n)] = normalise(msg{n}.pi .* msg{n}.lambda);
marginal{i,t} = bel;
end
end
loglik = 0;
%loglik = sum(log(lik));
%%%%%%%
function lambda = compute_lambda(n, cs, msg, ns)
% Pearl p183 eq 4.50
lambda = prod_lambda_msgs(n, cs, msg, ns);
%%%%%%%
function pi_msg = compute_pi_msg(n, cs, msg, c, ns)
% Pearl p183 eq 4.53 and 4.51
pi_msg = msg{n}.pi .* prod_lambda_msgs(n, cs, msg, ns, c);
%%%%%%%%%
function lam = prod_lambda_msgs(n, cs, msg, ns, except)
if nargin < 5, except = -1; end
%lam = msg{n}.lambda_from_self(:);
lam = ones(ns(n), 1);
for i=1:length(cs)
c = cs(i);
if c ~= except
lam = lam .* msg{n}.lambda_from_child{i};
end
end
%%%%%%%%%
function msg = init_msgs(dag, ns, evidence, eclass, CPD)
% INIT_MSGS Initialize the lambda/pi message and state vectors (pearl_dbn)
% msg = init_msgs(dag, ns, evidence)
N = length(dag);
msg = cell(1,N);
observed = ~isemptycell(evidence(:));
for n=1:N
ps = parents(dag, n);
msg{n}.pi_from_parent = cell(1, length(ps));
for i=1:length(ps)
p = ps(i);
msg{n}.pi_from_parent{i} = ones(ns(p), 1);
end
cs = children(dag, n);
msg{n}.lambda_from_child = cell(1, length(cs));
for i=1:length(cs)
c = cs(i);
msg{n}.lambda_from_child{i} = ones(ns(n), 1);
end
msg{n}.lambda = ones(ns(n), 1);
msg{n}.pi = ones(ns(n), 1);
% Initialize the lambdas with any evidence
if observed(n)
v = evidence{n};
msg{n}.lambda = zeros(ns(n), 1);
msg{n}.lambda(v) = 1; % delta function
msg{n}.lambda = [];
end
end
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