function [transmat, obsmat, exp_num_trans, exp_num_emit, gamma, ll] = online_em(...    prior, transmat, obsmat, exp_num_trans, exp_num_emit, decay, data, ...    act, adj_trans, adj_obs, dirichlet, filter_only)% ONLINE_EM Adjust the parameters using a weighted combination of the old and new expected statistics%% [transmat, obsmat, exp_num_trans, exp_num_emit, gamma, ll] = online_em(...%    prior, transmat, obsmat, exp_num_trans, exp_num_emit, decay, data, act, ...%    adj_trans, adj_obs, dirichlet, filter_only)% % 0 < decay < 1, with smaller values meaning the past is forgotten more quickly.% (We need to decay the old ess, since they were based on out-of-date parameters.)% The other params are as in learn_hmm.% We do a single forwards-backwards pass on the provided data, initializing with the specified prior.% (If filter_only = 1, we only do a forwards pass.)if ~exist('act'), act = []; endif ~exist('adj_trans'), adj_trans = 1; endif ~exist('adj_obs'), adj_obs = 1; endif ~exist('dirichlet'), dirichlet = 0; endif ~exist('filter_only'), filter_only = 0; end% E stepolikseq = mk_dhmm_obs_lik(data, obsmat);if isempty(act)  [alpha, beta, gamma, xi, ll] = forwards_backwards(prior, transmat, olikseq, filter_only);else  [alpha, beta, gamma, xi, ll] = forwards_backwards(prior, transmat, olikseq, [], [], act, filter_only);end% Increment ESS[S O] = size(obsmat);if adj_obs  exp_num_emit = decay*exp_num_emit + dirichlet*ones(S,O);  T = length(data);  if T < O    for t=1:T      o = data(t);      exp_num_emit(:,o) = exp_num_emit(:,o) + gamma(:,t);    end  else    for o=1:O      ndx = find(data==o);      if ~isempty(ndx)	exp_num_emit(:,o) = exp_num_emit(:,o) + sum(gamma(:, ndx), 2);      end    end  endendif adj_trans & (T > 1)  if isempty(act)    exp_num_trans = decay*exp_num_trans + sum(xi,3);  else    % act(2) determines Q(2), xi(:,:,1) holds P(Q(1), Q(2))    A = length(transmat);    for a=1:A      ndx = find(act(2:end)==a);      if ~isempty(ndx)	exp_num_trans{a} = decay*exp_num_trans{a} + sum(xi(:,:,ndx), 3);      end    end  endend% M stepif adj_obs  obsmat = mk_stochastic(exp_num_emit);endif adj_trans & (T>1)  if isempty(act)    transmat = mk_stochastic(exp_num_trans);  else    for a=1:A      transmat{a} = mk_stochastic(exp_num_trans{a});    end  endend