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% pigs model from Lauritzen and Nilsson, 2001
seed = 0;
rand('state', seed);
randn('state', seed);
% we number nodes down and to the right
h = [1 5 9 13];
t = [2 6 10];
d = [3 7 11];
u = [4 8 12 14];
N = 14;
dag = zeros(N);
% causal arcs
for i=1:3
dag(h(i), [t(i) h(i+1)]) = 1;
dag(d(i), [u(i) h(i+1)]) = 1;
end
dag(h(4), u(4)) = 1;
% information arcs
fig = 2;
switch fig
case 0,
% no info arcs
case 1,
% no-forgetting policy (figure 1)
for i=1:3
dag(t(i), d(i:3)) = 1;
end
case 2,
% reactive policy (figure 2)
for i=1:3
dag(t(i), d(i)) = 1;
end
case 7,
% omniscient policy (figure 7: di has access to hidden state h(i-1))
dag(t(1), d(1)) = 1;
for i=2:3
%dag([h(i-1) t(i-1) d(i-1)], d(i)) = 1;
dag([h(i-1) d(i-1)], d(i)) = 1; % t(i-1) is redundant given h(i-1)
end
end
ns = 2*ones(1,N);
ns(u) = 1;
% parameter tying
params = ones(1,N);
uparam = 1;
final_uparam = 2;
tparam = 3;
h1_param = 4;
hparam = 5;
dparams = 6:8;
params(u(1:3)) = uparam;
params(u(4)) = final_uparam;
params(t) = tparam;
params(h(1)) = h1_param;
params(h(2:end)) = hparam;
params(d) = dparams;
limid = mk_limid(dag, ns, 'chance', [h t], 'decision', d, 'utility', u, 'equiv_class', params);
% h = 1 means healthy, h = 2 means diseased
% d = 1 means don't treat, d = 2 means treat
% t = 1 means test shows healthy, t = 2 means test shows diseased
if 0
% use random params
limid.CPD{final_uparam} = tabular_utility_node(limid, u(4));
limid.CPD{uparam} = tabular_utility_node(limid, u(1));
limid.CPD{tparam} = tabular_CPD(limid, t(1));
limid.CPD{h1_param} = tabular_CPD(limid, h(1));
limid.CPD{hparam} = tabular_CPD(limid, h(2));
else
limid.CPD{final_uparam} = tabular_utility_node(limid, u(4), [1000 300]);
limid.CPD{uparam} = tabular_utility_node(limid, u(1), [0 -100]); % costs have negative utility!
% h P(t=1) P(t=2)
% 1 0.9 0.1
% 2 0.2 0.8
limid.CPD{tparam} = tabular_CPD(limid, t(1), [0.9 0.2 0.1 0.8]);
% P(h1)
limid.CPD{h1_param} = tabular_CPD(limid, h(1), [0.9 0.1]);
% hi di P(hj=1) P(hj=2), j = i+1, i=1:3
% 1 1 0.8 0.2
% 2 1 0.1 0.9
% 1 2 0.9 0.1
% 2 2 0.5 0.5
limid.CPD{hparam} = tabular_CPD(limid, h(2), [0.8 0.1 0.9 0.5 0.2 0.9 0.1 0.5]);
end
% Decision nodes get assigned uniform policies by default
for i=1:3
limid.CPD{dparams(i)} = tabular_decision_node(limid, d(i));
end
fname = '/home/cs/murphyk/matlab/Misc/loopybel.txt';
engines = {};
engines{end+1} = global_joint_inf_engine(limid);
engines{end+1} = jtree_limid_inf_engine(limid);
%engines{end+1} = belprop_inf_engine(limid, 'max_iter', 1*N, 'filename', fname, 'tol', 1e-3);
exact = [1 2];
%approx = 3;
approx = [];
max_iter = 1;
order = d(end:-1:1);
%order = d(1:end);
NE = length(engines);
MEU = zeros(1, NE);
niter = zeros(1, NE);
strategy = cell(1, NE);
for e=1:NE
[strategy{e}, MEU(e), niter(e)] = solve_limid(engines{e}, 'max_iter', max_iter, 'order', order);
end
MEU
% check results match those in the paper (p. 22)
direct_policy = eye(2); % treat iff test is positive
never_policy = [1 0; 1 0]; % never treat
tol = 1e-0; % results in paper are reported to 0dp
for e=exact(:)'
switch fig
case 2, % reactive policy
assert(approxeq(MEU(e), 727, tol));
assert(approxeq(strategy{e}{d(1)}(:), never_policy(:)))
assert(approxeq(strategy{e}{d(2)}(:), direct_policy(:)))
assert(approxeq(strategy{e}{d(3)}(:), direct_policy(:)))
case 1, assert(approxeq(MEU(e), 729, tol));
case 7, assert(approxeq(MEU(e), 732, tol));
end
end
for e=approx(:)'
for i=1:3
approxeq(strategy{exact(1)}{d(i)}, strategy{e}{d(i)})
dispcpt(strategy{e}{d(i)})
end
end
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