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1 function [transmat, obsmat, exp_num_trans, exp_num_emit, gamma, ll] = dhmm_em_online(...
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2 prior, transmat, obsmat, exp_num_trans, exp_num_emit, decay, data, ...
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3 act, adj_trans, adj_obs, dirichlet, filter_only)
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4 % ONLINE_EM Adjust the parameters using a weighted combination of the old and new expected statistics
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5 %
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6 % [transmat, obsmat, exp_num_trans, exp_num_emit, gamma, ll] = online_em(...
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7 % prior, transmat, obsmat, exp_num_trans, exp_num_emit, decay, data, act, ...
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8 % adj_trans, adj_obs, dirichlet, filter_only)
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9 %
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10 % 0 < decay < 1, with smaller values meaning the past is forgotten more quickly.
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11 % (We need to decay the old ess, since they were based on out-of-date parameters.)
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12 % The other params are as in learn_hmm.
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13 % We do a single forwards-backwards pass on the provided data, initializing with the specified prior.
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14 % (If filter_only = 1, we only do a forwards pass.)
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15
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16 if ~exist('act'), act = []; end
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17 if ~exist('adj_trans'), adj_trans = 1; end
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18 if ~exist('adj_obs'), adj_obs = 1; end
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19 if ~exist('dirichlet'), dirichlet = 0; end
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20 if ~exist('filter_only'), filter_only = 0; end
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21
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22 % E step
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23 olikseq = multinomial_prob(data, obsmat);
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24 if isempty(act)
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25 [alpha, beta, gamma, ll, xi] = fwdback(prior, transmat, olikseq, 'fwd_only', filter_only);
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26 else
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27 [alpha, beta, gamma, ll, xi] = fwdback(prior, transmat, olikseq, 'fwd_only', filter_only, ...
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28 'act', act);
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29 end
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30
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31 % Increment ESS
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32 [S O] = size(obsmat);
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33 if adj_obs
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34 exp_num_emit = decay*exp_num_emit + dirichlet*ones(S,O);
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35 T = length(data);
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36 if T < O
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37 for t=1:T
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38 o = data(t);
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39 exp_num_emit(:,o) = exp_num_emit(:,o) + gamma(:,t);
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40 end
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41 else
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42 for o=1:O
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43 ndx = find(data==o);
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44 if ~isempty(ndx)
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45 exp_num_emit(:,o) = exp_num_emit(:,o) + sum(gamma(:, ndx), 2);
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46 end
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47 end
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48 end
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49 end
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50
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51 if adj_trans & (T > 1)
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52 if isempty(act)
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53 exp_num_trans = decay*exp_num_trans + sum(xi,3);
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54 else
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55 % act(2) determines Q(2), xi(:,:,1) holds P(Q(1), Q(2))
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56 A = length(transmat);
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57 for a=1:A
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58 ndx = find(act(2:end)==a);
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59 if ~isempty(ndx)
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60 exp_num_trans{a} = decay*exp_num_trans{a} + sum(xi(:,:,ndx), 3);
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61 end
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62 end
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63 end
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64 end
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65
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66
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67 % M step
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68
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69 if adj_obs
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70 obsmat = mk_stochastic(exp_num_emit);
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71 end
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72 if adj_trans & (T>1)
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73 if isempty(act)
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74 transmat = mk_stochastic(exp_num_trans);
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75 else
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76 for a=1:A
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77 transmat{a} = mk_stochastic(exp_num_trans{a});
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78 end
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79 end
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80 end
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