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% Make a linear dynamical system
% X1 -> X2
% | |
% v v
% Y1 Y2
intra = zeros(2);
intra(1,2) = 1;
inter = zeros(2);
inter(1,1) = 1;
n = 2;
X = 2; % size of hidden state
Y = 2; % size of observable state
ns = [X Y];
dnodes = [];
onodes = [2];
eclass1 = [1 2];
eclass2 = [3 2];
bnet = mk_dbn(intra, inter, ns, 'discrete', dnodes, 'eclass1', eclass1, 'eclass2', eclass2, ...
'observed', onodes);
x0 = rand(X,1);
V0 = eye(X);
C0 = rand(Y,X);
R0 = eye(Y);
A0 = rand(X,X);
Q0 = eye(X);
bnet.CPD{1} = gaussian_CPD(bnet, 1, 'mean', x0, 'cov', V0, 'cov_prior_weight', 0);
bnet.CPD{2} = gaussian_CPD(bnet, 2, 'mean', zeros(Y,1), 'cov', R0, 'weights', C0, ...
'clamp_mean', 1, 'cov_prior_weight', 0);
bnet.CPD{3} = gaussian_CPD(bnet, 3, 'mean', zeros(X,1), 'cov', Q0, 'weights', A0, ...
'clamp_mean', 1, 'cov_prior_weight', 0);
T = 5; % fixed length sequences
clear engine;
engine{1} = kalman_inf_engine(bnet);
engine{2} = jtree_unrolled_dbn_inf_engine(bnet, T);
engine{3} = jtree_dbn_inf_engine(bnet);
N = length(engine);
% inference
ev = sample_dbn(bnet, T);
evidence = cell(n,T);
evidence(onodes,:) = ev(onodes, :);
t = 1;
query = [1 3];
m = cell(1, N);
ll = zeros(1, N);
for i=1:N
[engine{i}, ll(i)] = enter_evidence(engine{i}, evidence);
m{i} = marginal_nodes(engine{i}, query, t);
end
% compare all engines to engine{1}
for i=2:N
assert(approxeq(m{1}.mu, m{i}.mu));
assert(approxeq(m{1}.Sigma, m{i}.Sigma));
assert(approxeq(ll(1), ll(i)));
end
if 0
for i=2:N
approxeq(m{1}.mu, m{i}.mu)
approxeq(m{1}.Sigma, m{i}.Sigma)
approxeq(ll(1), ll(i))
end
end
% learning
ncases = 5;
cases = cell(1, ncases);
for i=1:ncases
ev = sample_dbn(bnet, T);
cases{i} = cell(n,T);
cases{i}(onodes,:) = ev(onodes, :);
end
max_iter = 2;
bnet2 = cell(1,N);
LLtrace = cell(1,N);
for i=1:N
[bnet2{i}, LLtrace{i}] = learn_params_dbn_em(engine{i}, cases, 'max_iter', max_iter);
end
for i=1:N
temp = bnet2{i};
for e=1:3
CPD{i,e} = struct(temp.CPD{e});
end
end
for i=2:N
assert(approxeq(LLtrace{i}, LLtrace{1}));
for e=1:3
assert(approxeq(CPD{i,e}.mean, CPD{1,e}.mean));
assert(approxeq(CPD{i,e}.cov, CPD{1,e}.cov));
assert(approxeq(CPD{i,e}.weights, CPD{1,e}.weights));
end
end
% Compare to KF toolbox
data = zeros(Y, T, ncases);
for i=1:ncases
data(:,:,i) = cell2num(cases{i}(onodes, :));
end
[A2, C2, Q2, R2, x2, V2, LL2trace] = learn_kalman(data, A0, C0, Q0, R0, x0, V0, max_iter);
e = 1;
assert(approxeq(x2, CPD{e,1}.mean))
assert(approxeq(V2, CPD{e,1}.cov))
assert(approxeq(C2, CPD{e,2}.weights))
assert(approxeq(R2, CPD{e,2}.cov));
assert(approxeq(A2, CPD{e,3}.weights))
assert(approxeq(Q2, CPD{e,3}.cov));
assert(approxeq(LL2trace, LLtrace{1}))
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