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1 function bnet = mk_map_hhmm(varargin)
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2
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3 % p is the prob of a successful move (defines the reliability of motors)
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4 p = 1;
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5 num_obs_nodes = 1;
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6
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7 for i=1:2:length(varargin)
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8 switch varargin{i},
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9 case 'p', p = varargin{i+1};
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10 case 'numobs', num_obs_node = varargin{i+1};
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11 end
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12 end
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13
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14
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15 q = 1-p;
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16
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17 % assign numbers to the nodes in topological order
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18 U = 1; A = 2; C = 3; F = 4; O = 5;
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19
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20 % create graph structure
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21
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22 ss = 5; % slice size
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23 intra = zeros(ss,ss);
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24 intra(U,F)=1;
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25 intra(A,[C F O])=1;
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26 intra(C,[F O])=1;
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27
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28 inter = zeros(ss,ss);
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29 inter(U,[A C])=1;
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30 inter(A,[A C])=1;
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31 inter(F,[A C])=1;
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32 inter(C,C)=1;
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33
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34 % node sizes
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35 ns = zeros(1,ss);
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36 ns(U) = 2; % left/right
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37 ns(A) = 2;
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38 ns(C) = 3;
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39 ns(F) = 2;
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40 ns(O) = 5; % we will assign each state a unique symbol
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41 l = 1; r = 2; % left/right
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42 L = 1; R = 2;
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43
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44 % Make the DBN
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45 bnet = mk_dbn(intra, inter, ns, 'observed', O);
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46 eclass = bnet.equiv_class;
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47
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48
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49
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50 % Define CPDs for slice 1
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51 % We clamp all of them, i.e., do not try to learn them.
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52
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53 % uniform probs over actions (the input could be chosen from a policy)
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54 bnet.CPD{eclass(U,1)} = tabular_CPD(bnet, U, 'CPT', mk_stochastic(ones(ns(U),1)), ...
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55 'adjustable', 0);
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56
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57 % uniform probs over starting abstract state
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58 bnet.CPD{eclass(A,1)} = tabular_CPD(bnet, A, 'CPT', mk_stochastic(ones(ns(A),1)), ...
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59 'adjustable', 0);
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60
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61 % Uniform probs over starting concrete state, modulo the fact
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62 % that corridor 2 is only of length 2.
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63 CPT = zeros(ns(A), ns(C)); % CPT(i,j) = P(C starts in j | A=i)
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64 CPT(1, :) = [1/3 1/3 1/3];
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65 CPT(2, :) = [1/2 1/2 0];
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66 bnet.CPD{eclass(C,1)} = tabular_CPD(bnet, C, 'CPT', CPT, 'adjustable', 0);
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67
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68 % Termination probs
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69 CPT = zeros(ns(U), ns(A), ns(C), ns(F));
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70 CPT(r,1,1,:) = [1 0];
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71 CPT(r,1,2,:) = [1 0];
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72 CPT(r,1,3,:) = [q p];
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73 CPT(r,2,1,:) = [1 0];
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74 CPT(r,2,2,:) = [q p];
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75 CPT(l,1,1,:) = [q p];
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76 CPT(l,1,2,:) = [1 0];
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77 CPT(l,1,3,:) = [1 0];
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78 CPT(l,2,1,:) = [q p];
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79 CPT(l,2,2,:) = [1 0];
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80
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81 bnet.CPD{eclass(F,1)} = tabular_CPD(bnet, F, 'CPT', CPT);
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82
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83
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84 % Assign each state a unique observation
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85 CPT = zeros(ns(A), ns(C), ns(O));
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86 CPT(1,1,1)=1;
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87 CPT(1,2,2)=1;
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88 CPT(1,3,3)=1;
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89 CPT(2,1,4)=1;
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90 CPT(2,2,5)=1;
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91 %CPT(2,3,:) undefined
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92
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93 bnet.CPD{eclass(O,1)} = tabular_CPD(bnet, O, 'CPT', CPT);
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94
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95
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96 % Define the CPDs for slice 2
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97
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98 % Abstract
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99
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100 % Since the top level never resets, the starting distribution is irrelevant:
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101 % A2 will be determined by sampling from transmat(A1,:).
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102 % But the code requires we specify it anyway; we make it all 0s, a dummy value.
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103 startprob = zeros(ns(U), ns(A));
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104
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105 transmat = zeros(ns(U), ns(A), ns(A));
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106 transmat(R,1,:) = [q p];
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107 transmat(R,2,:) = [0 1];
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108 transmat(L,1,:) = [1 0];
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109 transmat(L,2,:) = [p q];
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110
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111 % Qps are the parents we condition the parameters on, in this case just
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112 % the past action.
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113 bnet.CPD{eclass(A,2)} = hhmm2Q_CPD(bnet, A+ss, 'Fbelow', F, ...
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114 'startprob', startprob, 'transprob', transmat);
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115
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116
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117
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118 % Concrete
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119
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120 transmat = zeros(ns(C), ns(U), ns(A), ns(C));
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121 transmat(1,r,1,:) = [q p 0.0];
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122 transmat(2,r,1,:) = [0.0 q p];
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123 transmat(3,r,1,:) = [0.0 0.0 1.0];
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124 transmat(1,r,2,:) = [q p 0.0];
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125 transmat(2,r,2,:) = [0.0 1.0 0.0];
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126 %
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127 transmat(1,l,1,:) = [1.0 0.0 0.0];
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128 transmat(2,l,1,:) = [p q 0.0];
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129 transmat(3,l,1,:) = [0.0 p q];
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130 transmat(1,l,2,:) = [1.0 0.0 0.0];
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131 transmat(2,l,2,:) = [p q 0.0];
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132
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133 % Add a new dimension for A(t-1), by copying old vals,
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134 % so the matrix is the same size as startprob
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135
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136
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137 transmat = reshape(transmat, [ns(C) ns(U) ns(A) 1 ns(C)]);
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138 transmat = repmat(transmat, [1 1 1 ns(A) 1]);
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139
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140 % startprob(C(t-1), U(t-1), A(t-1), A(t), C(t))
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141 startprob = zeros(ns(C), ns(U), ns(A), ns(A), ns(C));
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142 startprob(1,L,1,1,:) = [1.0 0.0 0.0];
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143 startprob(3,R,1,2,:) = [1.0 0.0 0.0];
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144 startprob(3,R,1,1,:) = [0.0 0.0 1.0];
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145 %
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146 startprob(1,L,2,1,:) = [0.0 0.0 010];
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147 startprob(2,L,2,1,:) = [1.0 0.0 0.0];
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148 startprob(2,R,2,2,:) = [0.0 1.0 0.0];
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149
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150 % want transmat(U,A,C,At,Ct), ie. in topo order
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151 transmat = permute(transmat, [2 3 1 4 5]);
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152 startprob = permute(startprob, [2 3 1 4 5]);
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153 bnet.CPD{eclass(C,2)} = hhmm2Q_CPD(bnet, C+ss, 'Fself', F, ...
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154 'startprob', startprob, 'transprob', transmat);
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155
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156
|