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1 function bnet = mk_hhmm3(varargin)
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2 % MK_HHMM3 Make a 3 level Hierarchical HMM
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3 % bnet = mk_hhmm3(...)
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4 %
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5 % 3-layer hierarchical HMM where level 1 only connects to level 2, not 3 or obs.
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6 % This enforces sub-models (which differ only in their Q1 index) to be shared.
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7 % Also, we enforce the fact that each model always starts in its initial state
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8 % and only finishes in its final state. However, the prob. of finishing (as opposed to
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9 % self-transitioning to the final state) can be learned.
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10 % The fact that we always finish from the same state means we do not need to condition
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11 % F(i) on Q(i-1), since finishing prob is indep of calling context.
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12 %
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13 % The DBN is the same as Fig 10 in my tech report.
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14 %
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15 % Q1 ----------> Q1
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16 % | / |
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17 % | / |
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18 % | F2 ------- |
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19 % | ^ \ |
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20 % | /| \ |
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21 % v | v v
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22 % Q2-| --------> Q2
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23 % /| | ^
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24 % / | | /|
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25 % | | F3 ---------/ |
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26 % | | ^ \ |
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27 % | v / v
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28 % | Q3 -----------> Q3
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29 % | |
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30 % \ |
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31 % v v
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32 % O
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33 %
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34 %
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35 % Optional arguments in name/value format [default]
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36 %
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37 % Qsizes - sizes at each level [ none ]
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38 % Osize - size of O node [ none ]
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39 % discrete_obs - 1 means O is tabular_CPD, 0 means O is gaussian_CPD [0]
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40 % Oargs - cell array of args to pass to the O CPD [ {} ]
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41 % transprob1 - transprob1(i,j) = P(Q1(t)=j|Q1(t-1)=i) ['ergodic']
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42 % startprob1 - startprob1(j) = P(Q1(t)=j) ['leftstart']
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43 % transprob2 - transprob2(i,k,j) = P(Q2(t)=j|Q2(t-1)=i,Q1(t)=k) ['leftright']
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44 % startprob2 - startprob2(k,j) = P(Q2(t)=j|Q1(t)=k) ['leftstart']
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45 % termprob2 - termprob2(j,f) = P(F2(t)=f|Q2(t)=j) ['rightstop']
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46 % transprob3 - transprob3(i,k,j) = P(Q3(t)=j|Q3(t-1)=i,Q2(t)=k) ['leftright']
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47 % startprob3 - startprob3(k,j) = P(Q3(t)=j|Q2(t)=k) ['leftstart']
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48 % termprob3 - termprob3(j,f) = P(F3(t)=f|Q3(t)=j) ['rightstop']
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49 %
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50 % leftstart means the model always starts in state 1.
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51 % rightstop means the model always finished in its last state (Qsize(d)).
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52 %
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53 % Q1:Q3 in slice 1 are of type tabular_CPD
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54 % Q1:Q3 in slice 2 are of type hhmmQ_CPD.
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55 % F2 is of type hhmmF_CPD, F3 is of type tabular_CPD.
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56
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57 ss = 6; D = 3;
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58 Q1 = 1; Q2 = 2; Q3 = 3; F3 = 4; F2 = 5; obs = 6;
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59 Qnodes = [Q1 Q2 Q3]; Fnodes = [F2 F3];
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60 names = {'Q1', 'Q2', 'Q3', 'F3', 'F2', 'obs'};
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61
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62 intra = zeros(ss);
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63 intra(Q1, Q2) = 1;
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64 intra(Q2, [F2 Q3 obs]) = 1;
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65 intra(Q3, [F3 obs]) = 1;
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66 intra(F3, F2) = 1;
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67
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68 inter = zeros(ss);
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69 inter(Q1,Q1) = 1;
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70 inter(Q2,Q2) = 1;
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71 inter(Q3,Q3) = 1;
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72 inter(F2,[Q1 Q2]) = 1;
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73 inter(F3,[Q2 Q3]) = 1;
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74
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75
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76 % get sizes of nodes
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77 args = varargin;
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78 nargs = length(args);
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79 Qsizes = [];
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80 Osize = 0;
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81 for i=1:2:nargs
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82 switch args{i},
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83 case 'Qsizes', Qsizes = args{i+1};
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84 case 'Osize', Osize = args{i+1};
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85 end
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86 end
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87 if isempty(Qsizes), error('must specify Qsizes'); end
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88 if Osize==0, error('must specify Osize'); end
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89
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90 % set default params
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91 discrete_obs = 0;
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92 Oargs = {};
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93 startprob1 = 'ergodic';
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94 startprob2 = 'leftstart';
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95 startprob3 = 'leftstart';
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96 transprob1 = 'ergodic';
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97 transprob2 = 'leftright';
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98 transprob3 = 'leftright';
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99 termprob2 = 'rightstop';
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100 termprob3 = 'rightstop';
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101
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102
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103 for i=1:2:nargs
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104 switch args{i},
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105 case 'discrete_obs', discrete_obs = args{i+1};
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106 case 'Oargs', Oargs = args{i+1};
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107 case 'Q1args', Q1args = args{i+1};
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108 case 'Q2args', Q2args = args{i+1};
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109 case 'Q3args', Q3args = args{i+1};
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110 case 'F2args', F2args = args{i+1};
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111 case 'F3args', F3args = args{i+1};
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112 end
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113 end
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114
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115
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116 ns = zeros(1,ss);
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117 ns(Qnodes) = Qsizes;
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118 ns(obs) = Osize;
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119 ns(Fnodes) = 2;
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120
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121 dnodes = [Qnodes Fnodes];
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122 if discrete_obs
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123 dnodes = [dnodes obs];
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124 end
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125 onodes = [obs];
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126
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127 bnet = mk_dbn(intra, inter, ns, 'observed', onodes, 'discrete', dnodes, 'names', names);
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128 eclass = bnet.equiv_class;
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129
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130 if strcmp(startprob1, 'ergodic')
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131 startprob1 = normalise(ones(1,ns(Q1)));
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132 end
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133 if strcmp(startprob2, 'leftstart')
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134 startprob2 = zeros(ns(Q1), ns(Q2));
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135 starpbrob2(:, 1) = 1.0;
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136 end
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137 if strcmp(startprob3, 'leftstart')
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138 startprob3 = zeros(ns(Q2), ns(Q3));
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139 starpbrob3(:, 1) = 1.0;
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140 end
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141
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142 if strcmp(termprob2, 'rightstop')
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143 p = 0.9;
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144 termprob2 = zeros(Qsize(2),2);
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145 termprob2(:, 2) = p;
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146 termprob2(:, 1) = 1-p;
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147 termprob2(1:(Qsize(2)-1), 1) = 1;
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148 end
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149 if strcmp(termprob3, 'rightstop')
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150 p = 0.9;
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151 termprob3 = zeros(Qsize(3),2);
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152 termprob3(:, 2) = p;
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153 termprob3(:, 1) = 1-p;
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154 termprob3(1:(Qsize(3)-1), 1) = 1;
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155 end
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156
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157
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158 % SLICE 1
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159
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160 % We clamp untied nodes in the first slice, since their params can't be estimated
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161 % from just one sequence
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162
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163 bnet.CPD{eclass(Q1,1)} = tabular_CPD(bnet, Q1, 'CPT', startprob1, 'adjustable', 0);
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164 bnet.CPD{eclass(Q2,1)} = tabular_CPD(bnet, Q2, 'CPT', startprob2, 'adjustable', 0);
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165 bnet.CPD{eclass(Q3,1)} = tabular_CPD(bnet, Q3, 'CPT', startprob3, 'adjustable', 0);
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166
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167 bnet.CPD{eclass(F2,1)} = hhmmF_CPD(bnet, F2, Qnodes, 2, D, 'termprob', termprob2);
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168 bnet.CPD{eclass(F3,1)} = tabular_CPD(bnet, F3, 'CPT', termprob3);
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169
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170 if discrete_obs
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171 bnet.CPD{eclass(obs,1)} = tabular_CPD(bnet, obs, Oargs{:});
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172 else
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173 bnet.CPD{eclass(obs,1)} = gaussian_CPD(bnet, obs, Oargs{:});
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174 end
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175
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176 % SLICE 2
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177
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178 bnet.CPD{eclass(Q1,2)} = hhmmQ_CPD(bnet, Q1+ss, Qnodes, 1, D, 'transprob', transprob1, 'startprob', startprob1);
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179 bnet.CPD{eclass(Q2,2)} = hhmmQ_CPD(bnet, Q2+ss, Qnodes, 2, D, 'transprob', transprob2, 'startprob', startprob2);
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180 bnet.CPD{eclass(Q3,2)} = hhmmQ_CPD(bnet, Q3+ss, Qnodes, 3, D, 'transprob', transprob3, 'startprob', startprob3);
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181
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