comparison toolboxes/FullBNT-1.0.7/bnt/examples/dynamic/Old/kalman1.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% 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}))
+