Daniel@0: function CPD = maximize_params(CPD, temp)
Daniel@0: % MAXIMIZE_PARAMS Set the params of a CPD to their ML values (Gaussian)
Daniel@0: % CPD = maximize_params(CPD, temperature)
Daniel@0: %
Daniel@0: % Temperature is currently ignored.
Daniel@0: 
Daniel@0: if ~adjustable_CPD(CPD), return; end
Daniel@0: 
Daniel@0: CPD1 = struct(new_maximize_params(CPD));
Daniel@0: CPD2 = struct(old_maximize_params(CPD));
Daniel@0: assert(approxeq(CPD1.mean, CPD2.mean))
Daniel@0: assert(approxeq(CPD1.cov, CPD2.cov))
Daniel@0: assert(approxeq(CPD1.weights, CPD2.weights))
Daniel@0: 
Daniel@0: CPD = new_maximize_params(CPD);
Daniel@0: 
Daniel@0: %%%%%%%
Daniel@0: function CPD = new_maximize_params(CPD)
Daniel@0: 
Daniel@0: if CPD.clamped_mean
Daniel@0:   cl_mean = CPD.mean;
Daniel@0: else
Daniel@0:   cl_mean = [];
Daniel@0: end
Daniel@0: 
Daniel@0: if CPD.clamped_cov
Daniel@0:   cl_cov = CPD.cov;
Daniel@0: else
Daniel@0:   cl_cov = [];
Daniel@0: end
Daniel@0: 
Daniel@0: if CPD.clamped_weights
Daniel@0:   cl_weights = CPD.weights;
Daniel@0: else
Daniel@0:   cl_weights = [];
Daniel@0: end
Daniel@0: 
Daniel@0: [ssz psz Q] = size(CPD.weights);
Daniel@0: 
Daniel@0: prior =  repmat(CPD.cov_prior_weight*eye(ssz,ssz), [1 1 Q]);
Daniel@0: [CPD.mean, CPD.cov, CPD.weights] = ...
Daniel@0:     Mstep_clg('w', CPD.Wsum, 'YY', CPD.WYYsum, 'Y', CPD.WYsum, 'YTY', [], ...
Daniel@0: 	      'XX', CPD.WXXsum, 'XY', CPD.WXYsum, 'X', CPD.WXsum, ...
Daniel@0: 	      'cov_type', CPD.cov_type, 'clamped_mean', cl_mean, ...
Daniel@0: 	      'clamped_cov', cl_cov, 'clamped_weights', cl_weights, ...
Daniel@0: 	      'tied_cov', CPD.tied_cov, ...
Daniel@0: 	      'cov_prior', prior);
Daniel@0: 
Daniel@0: 
Daniel@0: %%%%%%%%%%%
Daniel@0: 
Daniel@0: function CPD = old_maximize_params(CPD)
Daniel@0: 
Daniel@0: 
Daniel@0: if ~adjustable_CPD(CPD), return; end
Daniel@0: 
Daniel@0: %assert(approxeq(CPD.nsamples, sum(CPD.Wsum)));
Daniel@0: assert(~any(isnan(CPD.WXXsum)))
Daniel@0: assert(~any(isnan(CPD.WXYsum)))
Daniel@0: assert(~any(isnan(CPD.WYYsum)))
Daniel@0: 
Daniel@0: [self_size cpsize dpsize] = size(CPD.weights);
Daniel@0: 
Daniel@0: % Append 1s to the parents, and derive the corresponding cross products.
Daniel@0: % This is used when estimate the means and weights simultaneosuly,
Daniel@0: % and when estimatting Sigma.
Daniel@0: % Let x2 = [x 1]'
Daniel@0: XY = zeros(cpsize+1, self_size, dpsize); % XY(:,:,i) = sum_l w(l,i) x2(l) y(l)' 
Daniel@0: XX = zeros(cpsize+1, cpsize+1, dpsize); % XX(:,:,i) = sum_l w(l,i) x2(l) x2(l)' 
Daniel@0: YY = zeros(self_size, self_size, dpsize); % YY(:,:,i) = sum_l w(l,i) y(l) y(l)' 
Daniel@0: for i=1:dpsize
Daniel@0:   XY(:,:,i) = [CPD.WXYsum(:,:,i) % X*Y
Daniel@0: 	       CPD.WYsum(:,i)']; % 1*Y
Daniel@0:   % [x  * [x' 1]  = [xx' x
Daniel@0:   %  1]              x'  1]
Daniel@0:   XX(:,:,i) = [CPD.WXXsum(:,:,i) CPD.WXsum(:,i);
Daniel@0: 	       CPD.WXsum(:,i)'   CPD.Wsum(i)];
Daniel@0:   YY(:,:,i) = CPD.WYYsum(:,:,i);
Daniel@0: end
Daniel@0: 
Daniel@0: w = CPD.Wsum(:);
Daniel@0: % Set any zeros to one before dividing
Daniel@0: % This is valid because w(i)=0 => WYsum(:,i)=0, etc
Daniel@0: w = w + (w==0);
Daniel@0: 
Daniel@0: if CPD.clamped_mean
Daniel@0:   % Estimating B2 and then setting the last column (the mean) to the clamped mean is *not* equivalent
Daniel@0:   % to estimating B and then adding the clamped_mean to the last column.
Daniel@0:   if ~CPD.clamped_weights
Daniel@0:     B = zeros(self_size, cpsize, dpsize);
Daniel@0:     for i=1:dpsize
Daniel@0:       if det(CPD.WXXsum(:,:,i))==0
Daniel@0: 	B(:,:,i) = 0;
Daniel@0:       else
Daniel@0: 	% Eqn 9 in table 2 of TR
Daniel@0: 	%B(:,:,i) = CPD.WXYsum(:,:,i)' * inv(CPD.WXXsum(:,:,i));
Daniel@0: 	B(:,:,i) = (CPD.WXXsum(:,:,i) \ CPD.WXYsum(:,:,i))';
Daniel@0:       end
Daniel@0:     end
Daniel@0:     %CPD.weights = reshape(B, [self_size cpsize dpsize]);
Daniel@0:     CPD.weights = B;
Daniel@0:   end
Daniel@0: elseif CPD.clamped_weights % KPM 1/25/02
Daniel@0:   if ~CPD.clamped_mean % ML estimate is just sample mean of the residuals
Daniel@0:     for i=1:dpsize
Daniel@0:       CPD.mean(:,i) = (CPD.WYsum(:,i) - CPD.weights(:,:,i) * CPD.WXsum(:,i)) / w(i);
Daniel@0:     end
Daniel@0:   end
Daniel@0: else % nothing is clamped, so estimate mean and weights simultaneously
Daniel@0:   B2 = zeros(self_size, cpsize+1, dpsize);
Daniel@0:   for i=1:dpsize
Daniel@0:     if det(XX(:,:,i))==0  % fix by U. Sondhauss 6/27/99
Daniel@0:       B2(:,:,i)=0;          
Daniel@0:     else                    
Daniel@0:       % Eqn 9 in table 2 of TR
Daniel@0:       %B2(:,:,i) = XY(:,:,i)' * inv(XX(:,:,i));
Daniel@0:       B2(:,:,i) = (XX(:,:,i) \ XY(:,:,i))';
Daniel@0:     end                   
Daniel@0:     CPD.mean(:,i) = B2(:,cpsize+1,i);
Daniel@0:     CPD.weights(:,:,i) = B2(:,1:cpsize,i);
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: % Let B2 = [W mu]
Daniel@0: if cpsize>0
Daniel@0:   B2(:,1:cpsize,:) = reshape(CPD.weights, [self_size cpsize dpsize]);
Daniel@0: end
Daniel@0: B2(:,cpsize+1,:) = reshape(CPD.mean, [self_size dpsize]);
Daniel@0: 
Daniel@0: % To avoid singular covariance matrices,
Daniel@0: % we use the regularization method suggested in "A Quasi-Bayesian approach to estimating
Daniel@0: % parameters for mixtures of normal distributions", Hamilton 91.
Daniel@0: % If the ML estimate is Sigma = M/N, the MAP estimate is (M+gamma*I) / (N+gamma),
Daniel@0: % where gamma >=0 is a smoothing parameter (equivalent sample size of I prior)
Daniel@0: 
Daniel@0: gamma = CPD.cov_prior_weight;
Daniel@0: 
Daniel@0: if ~CPD.clamped_cov
Daniel@0:   if CPD.cov_prior_entropic % eqn 12 of Brand AI/Stat 99
Daniel@0:     Z = 1-temp;
Daniel@0:     % When temp > 1, Z is negative, so we are dividing by a smaller
Daniel@0:     % number, ie. increasing the variance.
Daniel@0:   else
Daniel@0:     Z = 0;
Daniel@0:   end
Daniel@0:   if CPD.tied_cov
Daniel@0:     S = zeros(self_size, self_size);
Daniel@0:     % Eqn 2 from table 2 in TR
Daniel@0:     for i=1:dpsize
Daniel@0:       S = S + (YY(:,:,i) - B2(:,:,i)*XY(:,:,i));
Daniel@0:     end
Daniel@0:     %denom = CPD.nsamples + gamma + Z;
Daniel@0:     denom = CPD.nsamples +  Z;
Daniel@0:     S = (S + gamma*eye(self_size)) / denom;
Daniel@0:     if strcmp(CPD.cov_type, 'diag')
Daniel@0:       S = diag(diag(S));
Daniel@0:     end
Daniel@0:     CPD.cov = repmat(S, [1 1 dpsize]);
Daniel@0:   else 
Daniel@0:     for i=1:dpsize      
Daniel@0:       % Eqn 1 from table 2 in TR
Daniel@0:       S = YY(:,:,i) - B2(:,:,i)*XY(:,:,i);
Daniel@0:       %denom = w(i) + gamma + Z;
Daniel@0:       denom = w(i) + Z;
Daniel@0:       S = (S + gamma*eye(self_size)) / denom;
Daniel@0:       CPD.cov(:,:,i) = S;
Daniel@0:     end
Daniel@0:     if strcmp(CPD.cov_type, 'diag')
Daniel@0:       for i=1:dpsize      
Daniel@0: 	CPD.cov(:,:,i) = diag(diag(CPD.cov(:,:,i)));
Daniel@0:       end
Daniel@0:     end
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: check_covars = 0;
Daniel@0: min_covar = 1e-5;
Daniel@0: if check_covars % prevent collapsing to a point
Daniel@0:   for i=1:dpsize
Daniel@0:     if min(svd(CPD.cov(:,:,i))) < min_covar
Daniel@0:       disp(['resetting singular covariance for node ' num2str(CPD.self)]);
Daniel@0:       CPD.cov(:,:,i) = CPD.init_cov(:,:,i);
Daniel@0:     end
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: