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

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first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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wolffd@0 1 % Make a linear dynamical system
wolffd@0 2 % X1 -> X2
wolffd@0 3 % | |
wolffd@0 4 % v v
wolffd@0 5 % Y1 Y2
wolffd@0 6
wolffd@0 7 intra = zeros(2);
wolffd@0 8 intra(1,2) = 1;
wolffd@0 9 inter = zeros(2);
wolffd@0 10 inter(1,1) = 1;
wolffd@0 11 n = 2;
wolffd@0 12
wolffd@0 13 X = 2; % size of hidden state
wolffd@0 14 Y = 2; % size of observable state
wolffd@0 15
wolffd@0 16 ns = [X Y];
wolffd@0 17 dnodes = [];
wolffd@0 18 onodes = [2];
wolffd@0 19 eclass1 = [1 2];
wolffd@0 20 eclass2 = [3 2];
wolffd@0 21 bnet = mk_dbn(intra, inter, ns, 'discrete', dnodes, 'eclass1', eclass1, 'eclass2', eclass2, ...
wolffd@0 22 'observed', onodes);
wolffd@0 23
wolffd@0 24 x0 = rand(X,1);
wolffd@0 25 V0 = eye(X);
wolffd@0 26 C0 = rand(Y,X);
wolffd@0 27 R0 = eye(Y);
wolffd@0 28 A0 = rand(X,X);
wolffd@0 29 Q0 = eye(X);
wolffd@0 30
wolffd@0 31 bnet.CPD{1} = gaussian_CPD(bnet, 1, 'mean', x0, 'cov', V0, 'cov_prior_weight', 0);
wolffd@0 32 bnet.CPD{2} = gaussian_CPD(bnet, 2, 'mean', zeros(Y,1), 'cov', R0, 'weights', C0, ...
wolffd@0 33 'clamp_mean', 1, 'cov_prior_weight', 0);
wolffd@0 34 bnet.CPD{3} = gaussian_CPD(bnet, 3, 'mean', zeros(X,1), 'cov', Q0, 'weights', A0, ...
wolffd@0 35 'clamp_mean', 1, 'cov_prior_weight', 0);
wolffd@0 36
wolffd@0 37
wolffd@0 38 T = 5; % fixed length sequences
wolffd@0 39
wolffd@0 40 clear engine;
wolffd@0 41 engine{1} = kalman_inf_engine(bnet);
wolffd@0 42 engine{2} = jtree_unrolled_dbn_inf_engine(bnet, T);
wolffd@0 43 engine{3} = jtree_dbn_inf_engine(bnet);
wolffd@0 44 N = length(engine);
wolffd@0 45
wolffd@0 46 % inference
wolffd@0 47
wolffd@0 48 ev = sample_dbn(bnet, T);
wolffd@0 49 evidence = cell(n,T);
wolffd@0 50 evidence(onodes,:) = ev(onodes, :);
wolffd@0 51
wolffd@0 52 t = 1;
wolffd@0 53 query = [1 3];
wolffd@0 54 m = cell(1, N);
wolffd@0 55 ll = zeros(1, N);
wolffd@0 56 for i=1:N
wolffd@0 57 [engine{i}, ll(i)] = enter_evidence(engine{i}, evidence);
wolffd@0 58 m{i} = marginal_nodes(engine{i}, query, t);
wolffd@0 59 end
wolffd@0 60
wolffd@0 61 % compare all engines to engine{1}
wolffd@0 62 for i=2:N
wolffd@0 63 assert(approxeq(m{1}.mu, m{i}.mu));
wolffd@0 64 assert(approxeq(m{1}.Sigma, m{i}.Sigma));
wolffd@0 65 assert(approxeq(ll(1), ll(i)));
wolffd@0 66 end
wolffd@0 67
wolffd@0 68 if 0
wolffd@0 69 for i=2:N
wolffd@0 70 approxeq(m{1}.mu, m{i}.mu)
wolffd@0 71 approxeq(m{1}.Sigma, m{i}.Sigma)
wolffd@0 72 approxeq(ll(1), ll(i))
wolffd@0 73 end
wolffd@0 74 end
wolffd@0 75
wolffd@0 76 % learning
wolffd@0 77
wolffd@0 78 ncases = 5;
wolffd@0 79 cases = cell(1, ncases);
wolffd@0 80 for i=1:ncases
wolffd@0 81 ev = sample_dbn(bnet, T);
wolffd@0 82 cases{i} = cell(n,T);
wolffd@0 83 cases{i}(onodes,:) = ev(onodes, :);
wolffd@0 84 end
wolffd@0 85
wolffd@0 86 max_iter = 2;
wolffd@0 87 bnet2 = cell(1,N);
wolffd@0 88 LLtrace = cell(1,N);
wolffd@0 89 for i=1:N
wolffd@0 90 [bnet2{i}, LLtrace{i}] = learn_params_dbn_em(engine{i}, cases, 'max_iter', max_iter);
wolffd@0 91 end
wolffd@0 92
wolffd@0 93 for i=1:N
wolffd@0 94 temp = bnet2{i};
wolffd@0 95 for e=1:3
wolffd@0 96 CPD{i,e} = struct(temp.CPD{e});
wolffd@0 97 end
wolffd@0 98 end
wolffd@0 99
wolffd@0 100 for i=2:N
wolffd@0 101 assert(approxeq(LLtrace{i}, LLtrace{1}));
wolffd@0 102 for e=1:3
wolffd@0 103 assert(approxeq(CPD{i,e}.mean, CPD{1,e}.mean));
wolffd@0 104 assert(approxeq(CPD{i,e}.cov, CPD{1,e}.cov));
wolffd@0 105 assert(approxeq(CPD{i,e}.weights, CPD{1,e}.weights));
wolffd@0 106 end
wolffd@0 107 end
wolffd@0 108
wolffd@0 109
wolffd@0 110 % Compare to KF toolbox
wolffd@0 111
wolffd@0 112 data = zeros(Y, T, ncases);
wolffd@0 113 for i=1:ncases
wolffd@0 114 data(:,:,i) = cell2num(cases{i}(onodes, :));
wolffd@0 115 end
wolffd@0 116 [A2, C2, Q2, R2, x2, V2, LL2trace] = learn_kalman(data, A0, C0, Q0, R0, x0, V0, max_iter);
wolffd@0 117
wolffd@0 118
wolffd@0 119 e = 1;
wolffd@0 120 assert(approxeq(x2, CPD{e,1}.mean))
wolffd@0 121 assert(approxeq(V2, CPD{e,1}.cov))
wolffd@0 122 assert(approxeq(C2, CPD{e,2}.weights))
wolffd@0 123 assert(approxeq(R2, CPD{e,2}.cov));
wolffd@0 124 assert(approxeq(A2, CPD{e,3}.weights))
wolffd@0 125 assert(approxeq(Q2, CPD{e,3}.cov));
wolffd@0 126 assert(approxeq(LL2trace, LLtrace{1}))
wolffd@0 127