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