wolffd@0: function CPD = maximize_params(CPD, temp)
wolffd@0: % MAXIMIZE_PARAMS Set the params of a CPD to their ML values (Gaussian)
wolffd@0: % CPD = maximize_params(CPD, temperature)
wolffd@0: %
wolffd@0: % Temperature is currently only used for entropic prior on Sigma
wolffd@0: 
wolffd@0: % For details, see "Fitting a Conditional Gaussian Distribution", Kevin Murphy, tech. report,
wolffd@0: % 1998, available at www.cs.berkeley.edu/~murphyk/papers.html
wolffd@0: % Refering to table 2, we use equations 1/2 to estimate the covariance matrix in the untied/tied case,
wolffd@0: % and equation 9 to estimate the weight matrix and mean.
wolffd@0: % We do not implement spherical Gaussians - the code is already pretty complicated!
wolffd@0: 
wolffd@0: if ~adjustable_CPD(CPD), return; end
wolffd@0: 
wolffd@0: %assert(approxeq(CPD.nsamples, sum(CPD.Wsum)));
wolffd@0: assert(~any(isnan(CPD.WXXsum)))
wolffd@0: assert(~any(isnan(CPD.WXYsum)))
wolffd@0: assert(~any(isnan(CPD.WYYsum)))
wolffd@0: 
wolffd@0: [self_size cpsize dpsize] = size(CPD.weights);
wolffd@0: 
wolffd@0: % Append 1s to the parents, and derive the corresponding cross products.
wolffd@0: % This is used when estimate the means and weights simultaneosuly,
wolffd@0: % and when estimatting Sigma.
wolffd@0: % Let x2 = [x 1]'
wolffd@0: XY = zeros(cpsize+1, self_size, dpsize); % XY(:,:,i) = sum_l w(l,i) x2(l) y(l)' 
wolffd@0: XX = zeros(cpsize+1, cpsize+1, dpsize); % XX(:,:,i) = sum_l w(l,i) x2(l) x2(l)' 
wolffd@0: YY = zeros(self_size, self_size, dpsize); % YY(:,:,i) = sum_l w(l,i) y(l) y(l)' 
wolffd@0: for i=1:dpsize
wolffd@0:   XY(:,:,i) = [CPD.WXYsum(:,:,i) % X*Y
wolffd@0: 	       CPD.WYsum(:,i)']; % 1*Y
wolffd@0:   % [x  * [x' 1]  = [xx' x
wolffd@0:   %  1]              x'  1]
wolffd@0:   XX(:,:,i) = [CPD.WXXsum(:,:,i) CPD.WXsum(:,i);
wolffd@0: 	       CPD.WXsum(:,i)'   CPD.Wsum(i)];
wolffd@0:   YY(:,:,i) = CPD.WYYsum(:,:,i);
wolffd@0: end
wolffd@0: 
wolffd@0: w = CPD.Wsum(:);
wolffd@0: % Set any zeros to one before dividing
wolffd@0: % This is valid because w(i)=0 => WYsum(:,i)=0, etc
wolffd@0: w = w + (w==0);
wolffd@0: 
wolffd@0: if CPD.clamped_mean
wolffd@0:   % Estimating B2 and then setting the last column (the mean) to the clamped mean is *not* equivalent
wolffd@0:   % to estimating B and then adding the clamped_mean to the last column.
wolffd@0:   if ~CPD.clamped_weights
wolffd@0:     B = zeros(self_size, cpsize, dpsize);
wolffd@0:     for i=1:dpsize
wolffd@0:       if det(CPD.WXXsum(:,:,i))==0
wolffd@0: 	B(:,:,i) = 0;
wolffd@0:       else
wolffd@0: 	% Eqn 9 in table 2 of TR
wolffd@0: 	%B(:,:,i) = CPD.WXYsum(:,:,i)' * inv(CPD.WXXsum(:,:,i));
wolffd@0: 	B(:,:,i) = (CPD.WXXsum(:,:,i) \ CPD.WXYsum(:,:,i))';
wolffd@0:       end
wolffd@0:     end
wolffd@0:     %CPD.weights = reshape(B, [self_size cpsize dpsize]);
wolffd@0:     CPD.weights = B;
wolffd@0:   end
wolffd@0: elseif CPD.clamped_weights % KPM 1/25/02
wolffd@0:   if ~CPD.clamped_mean % ML estimate is just sample mean of the residuals
wolffd@0:     for i=1:dpsize
wolffd@0:       CPD.mean(:,i) = (CPD.WYsum(:,i) - CPD.weights(:,:,i) * CPD.WXsum(:,i)) / w(i);
wolffd@0:     end
wolffd@0:   end
wolffd@0: else % nothing is clamped, so estimate mean and weights simultaneously
wolffd@0:   B2 = zeros(self_size, cpsize+1, dpsize);
wolffd@0:   for i=1:dpsize
wolffd@0:     if det(XX(:,:,i))==0  % fix by U. Sondhauss 6/27/99
wolffd@0:       B2(:,:,i)=0;          
wolffd@0:     else                    
wolffd@0:       % Eqn 9 in table 2 of TR
wolffd@0:       %B2(:,:,i) = XY(:,:,i)' * inv(XX(:,:,i));
wolffd@0:       B2(:,:,i) = (XX(:,:,i) \ XY(:,:,i))';
wolffd@0:     end                   
wolffd@0:     CPD.mean(:,i) = B2(:,cpsize+1,i);
wolffd@0:     CPD.weights(:,:,i) = B2(:,1:cpsize,i);
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: % Let B2 = [W mu]
wolffd@0: if cpsize>0
wolffd@0:   B2(:,1:cpsize,:) = reshape(CPD.weights, [self_size cpsize dpsize]);
wolffd@0: end
wolffd@0: B2(:,cpsize+1,:) = reshape(CPD.mean, [self_size dpsize]);
wolffd@0: 
wolffd@0: % To avoid singular covariance matrices,
wolffd@0: % we use the regularization method suggested in "A Quasi-Bayesian approach to estimating
wolffd@0: % parameters for mixtures of normal distributions", Hamilton 91.
wolffd@0: % If the ML estimate is Sigma = M/N, the MAP estimate is (M+gamma*I) / (N+gamma),
wolffd@0: % where gamma >=0 is a smoothing parameter (equivalent sample size of I prior)
wolffd@0: 
wolffd@0: gamma = CPD.cov_prior_weight;
wolffd@0: 
wolffd@0: if ~CPD.clamped_cov
wolffd@0:   if CPD.cov_prior_entropic % eqn 12 of Brand AI/Stat 99
wolffd@0:     Z = 1-temp;
wolffd@0:     % When temp > 1, Z is negative, so we are dividing by a smaller
wolffd@0:     % number, ie. increasing the variance.
wolffd@0:   else
wolffd@0:     Z = 0;
wolffd@0:   end
wolffd@0:   if CPD.tied_cov
wolffd@0:     S = zeros(self_size, self_size);
wolffd@0:     % Eqn 2 from table 2 in TR
wolffd@0:     for i=1:dpsize
wolffd@0:       S = S + (YY(:,:,i) - B2(:,:,i)*XY(:,:,i));
wolffd@0:     end
wolffd@0:     %denom = max(1, CPD.nsamples + gamma + Z);
wolffd@0:     denom = CPD.nsamples + gamma + Z;
wolffd@0:     S = (S + gamma*eye(self_size)) / denom;
wolffd@0:     if strcmp(CPD.cov_type, 'diag')
wolffd@0:       S = diag(diag(S));
wolffd@0:     end
wolffd@0:     CPD.cov = repmat(S, [1 1 dpsize]);
wolffd@0:   else 
wolffd@0:     for i=1:dpsize      
wolffd@0:       % Eqn 1 from table 2 in TR
wolffd@0:       S = YY(:,:,i) - B2(:,:,i)*XY(:,:,i);
wolffd@0:       %denom = max(1, w(i) + gamma + Z); % gives wrong answers on mhmm1
wolffd@0:       denom = w(i) + gamma + Z;
wolffd@0:       S = (S + gamma*eye(self_size)) / denom;
wolffd@0:       CPD.cov(:,:,i) = S;
wolffd@0:     end
wolffd@0:     if strcmp(CPD.cov_type, 'diag')
wolffd@0:       for i=1:dpsize      
wolffd@0: 	CPD.cov(:,:,i) = diag(diag(CPD.cov(:,:,i)));
wolffd@0:       end
wolffd@0:     end
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: check_covars = 0;
wolffd@0: min_covar = 1e-5;
wolffd@0: if check_covars % prevent collapsing to a point
wolffd@0:   for i=1:dpsize
wolffd@0:     if min(svd(CPD.cov(:,:,i))) < min_covar
wolffd@0:       disp(['resetting singular covariance for node ' num2str(CPD.self)]);
wolffd@0:       CPD.cov(:,:,i) = CPD.init_cov(:,:,i);
wolffd@0:     end
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: