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1 % Make the HHMM in Figure 1 of the NIPS'01 paper
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2
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3 Qsize = [2 3 2];
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4 D = 3;
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5
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6 % transprob{d}(i,k,j), transprob{1}(i,j)
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7 % termprob{d}(k,j), termprob{1}(1,j)
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8 % startprob{d}(k,j), startprob{1}(1,j)
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9 % obsprob(k, o) for discrete outputs
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10
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11 % LEVEL 1
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12 % 1 2 e
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13 A{1} = [0 0 1;
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14 0 0 1];
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15 [transprob{1}, termprob{1}] = remove_hhmm_end_state(A{1});
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16 startprob{1} = [0.5 0.5];
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17 Q1args = {'startprob', startprob{1}, 'transprob', transprob{1}};
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18
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19 % LEVEL 2
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20 A{2} = zeros(Qsize(2), Qsize(1), Qsize(2)+1);
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21
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22 % 1 2 3 e
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23 A{2}(:,1,:) = [0 1 0 0
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24 0 0 1 0
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25 0 0 0 1];
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26
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27 % 1 2 3 e
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28 A{2}(:,2,:) = [0 1 0 0
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29 0 0 1 0
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30 0 0 0 1];
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31
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32 [transprob{2}, termprob{2}] = remove_hhmm_end_state(A{2});
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33
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34 % always enter level 2 in state 1
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35 startprob{2} = [1 0 0
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36 1 0 0];
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37
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38 Q2args = {'startprob', startprob{2}, 'transprob', transprob{2}};
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39 F2args = {'CPT', termprob{2}};
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40
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41
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42 % LEVEL 3
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43
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44 A{3} = zeros([Qsize(3) Qsize(1:2) Qsize(3)+1]);
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45 endstate = Qsize(3)+1;
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46 % Qt-1(3) Qt(1) Qt(2) Qt(3)
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47 % 1 2 e
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48 A{3}(1, 1, 1, endstate) = 1.0;
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49 A{3}(:, 1, 2, :) = [0.0 1.0 0.0
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50 0.5 0.0 0.5];
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51 A{3}(1, 1, 3, endstate) = 1.0;
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52
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53 A{3}(1, 2, 1, endstate) = 1.0;
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54 A{3}(:, 2, 2, :) = [0.0 1.0 0.0
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55 0.5 0.0 0.5];
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56 A{3}(1, 2, 3, endstate) = 1.0;
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57
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58 A{3} = reshape(A{3}, [Qsize(3) prod(Qsize(1:2)) Qsize(3)+1]);
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59 [transprob{3}, termprob{3}] = remove_hhmm_end_state(A{3});
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60
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61 % define the vertical entry points to level 3
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62 startprob{3} = zeros(Qsize);
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63 % Q1 Q2 Q3
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64 startprob{3}(1, 1, 1) = 1.0;
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65 startprob{3}(1, 2, 1) = 1.0;
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66 startprob{3}(1, 3, 1) = 1.0;
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67
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68 startprob{3}(2, 1, 1) = 1.0;
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69 startprob{3}(2, 2, 1) = 1.0;
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70 startprob{3}(2, 3, 1) = 1.0;
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71
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72 startprob{3} = reshape(startprob{3}, prod(Qsize(1:2)), Qsize(3));
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73
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74 chars = ['a', 'b', 'c', 'd', 'x', 'y'];
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75 Osize = length(chars);
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76
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77 obsprob = zeros([Qsize Osize]);
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78 % 1 2 3 O
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79 obsprob(1,1,1,find(chars == 'a')) = 1.0;
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80
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81 obsprob(1,2,1,find(chars == 'x')) = 1.0;
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82 obsprob(1,2,2,find(chars == 'y')) = 1.0;
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83
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84 obsprob(1,3,1,find(chars == 'b')) = 1.0;
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85
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86 obsprob(2,1,1,find(chars == 'c')) = 1.0;
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87
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88 obsprob(2,2,1,find(chars == 'x')) = 1.0;
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89 obsprob(2,2,2,find(chars == 'y')) = 1.0;
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90
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91 obsprob(2,3,1,find(chars == 'd')) = 1.0;
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92
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93 obsprob = reshape(obsprob, prod(Qsize), Osize);
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94
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95 [intra, inter, Qnodes, Fnodes, Onode] = mk_hhmm_topo(D);
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96
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97 hhmm.Qnodes = Qnodes;
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98 hhmm.Fnodes = Fnodes;
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99 hhmm.Onode = Onode;
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100 hhmm.D = D;
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101 hhmm.Qsize = Qsize;
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102 hhmm.Osize = Osize;
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103 hhmm.startprob = startprob;
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104 hhmm.transprob = transprob;
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105 hhmm.termprob = termprob;
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106 hhmm.obsprob = obsprob;
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107 hhmm.A = A;
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108
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109
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