Mercurial > hg > camir-aes2014
diff toolboxes/FullBNT-1.0.7/bnt/CPDs/@gaussian_CPD/Old/maximize_params.m @ 0:e9a9cd732c1e tip
first hg version after svn
author | wolffd |
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date | Tue, 10 Feb 2015 15:05:51 +0000 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/toolboxes/FullBNT-1.0.7/bnt/CPDs/@gaussian_CPD/Old/maximize_params.m Tue Feb 10 15:05:51 2015 +0000 @@ -0,0 +1,147 @@ +function CPD = maximize_params(CPD, temp) +% MAXIMIZE_PARAMS Set the params of a CPD to their ML values (Gaussian) +% CPD = maximize_params(CPD, temperature) +% +% Temperature is currently only used for entropic prior on Sigma + +% For details, see "Fitting a Conditional Gaussian Distribution", Kevin Murphy, tech. report, +% 1998, available at www.cs.berkeley.edu/~murphyk/papers.html +% Refering to table 2, we use equations 1/2 to estimate the covariance matrix in the untied/tied case, +% and equation 9 to estimate the weight matrix and mean. +% We do not implement spherical Gaussians - the code is already pretty complicated! + +if ~adjustable_CPD(CPD), return; end + +%assert(approxeq(CPD.nsamples, sum(CPD.Wsum))); +assert(~any(isnan(CPD.WXXsum))) +assert(~any(isnan(CPD.WXYsum))) +assert(~any(isnan(CPD.WYYsum))) + +[self_size cpsize dpsize] = size(CPD.weights); + +% Append 1s to the parents, and derive the corresponding cross products. +% This is used when estimate the means and weights simultaneosuly, +% and when estimatting Sigma. +% Let x2 = [x 1]' +XY = zeros(cpsize+1, self_size, dpsize); % XY(:,:,i) = sum_l w(l,i) x2(l) y(l)' +XX = zeros(cpsize+1, cpsize+1, dpsize); % XX(:,:,i) = sum_l w(l,i) x2(l) x2(l)' +YY = zeros(self_size, self_size, dpsize); % YY(:,:,i) = sum_l w(l,i) y(l) y(l)' +for i=1:dpsize + XY(:,:,i) = [CPD.WXYsum(:,:,i) % X*Y + CPD.WYsum(:,i)']; % 1*Y + % [x * [x' 1] = [xx' x + % 1] x' 1] + XX(:,:,i) = [CPD.WXXsum(:,:,i) CPD.WXsum(:,i); + CPD.WXsum(:,i)' CPD.Wsum(i)]; + YY(:,:,i) = CPD.WYYsum(:,:,i); +end + +w = CPD.Wsum(:); +% Set any zeros to one before dividing +% This is valid because w(i)=0 => WYsum(:,i)=0, etc +w = w + (w==0); + +if CPD.clamped_mean + % Estimating B2 and then setting the last column (the mean) to the clamped mean is *not* equivalent + % to estimating B and then adding the clamped_mean to the last column. + if ~CPD.clamped_weights + B = zeros(self_size, cpsize, dpsize); + for i=1:dpsize + if det(CPD.WXXsum(:,:,i))==0 + B(:,:,i) = 0; + else + % Eqn 9 in table 2 of TR + %B(:,:,i) = CPD.WXYsum(:,:,i)' * inv(CPD.WXXsum(:,:,i)); + B(:,:,i) = (CPD.WXXsum(:,:,i) \ CPD.WXYsum(:,:,i))'; + end + end + %CPD.weights = reshape(B, [self_size cpsize dpsize]); + CPD.weights = B; + end +elseif CPD.clamped_weights % KPM 1/25/02 + if ~CPD.clamped_mean % ML estimate is just sample mean of the residuals + for i=1:dpsize + CPD.mean(:,i) = (CPD.WYsum(:,i) - CPD.weights(:,:,i) * CPD.WXsum(:,i)) / w(i); + end + end +else % nothing is clamped, so estimate mean and weights simultaneously + B2 = zeros(self_size, cpsize+1, dpsize); + for i=1:dpsize + if det(XX(:,:,i))==0 % fix by U. Sondhauss 6/27/99 + B2(:,:,i)=0; + else + % Eqn 9 in table 2 of TR + %B2(:,:,i) = XY(:,:,i)' * inv(XX(:,:,i)); + B2(:,:,i) = (XX(:,:,i) \ XY(:,:,i))'; + end + CPD.mean(:,i) = B2(:,cpsize+1,i); + CPD.weights(:,:,i) = B2(:,1:cpsize,i); + end +end + +% Let B2 = [W mu] +if cpsize>0 + B2(:,1:cpsize,:) = reshape(CPD.weights, [self_size cpsize dpsize]); +end +B2(:,cpsize+1,:) = reshape(CPD.mean, [self_size dpsize]); + +% To avoid singular covariance matrices, +% we use the regularization method suggested in "A Quasi-Bayesian approach to estimating +% parameters for mixtures of normal distributions", Hamilton 91. +% If the ML estimate is Sigma = M/N, the MAP estimate is (M+gamma*I) / (N+gamma), +% where gamma >=0 is a smoothing parameter (equivalent sample size of I prior) + +gamma = CPD.cov_prior_weight; + +if ~CPD.clamped_cov + if CPD.cov_prior_entropic % eqn 12 of Brand AI/Stat 99 + Z = 1-temp; + % When temp > 1, Z is negative, so we are dividing by a smaller + % number, ie. increasing the variance. + else + Z = 0; + end + if CPD.tied_cov + S = zeros(self_size, self_size); + % Eqn 2 from table 2 in TR + for i=1:dpsize + S = S + (YY(:,:,i) - B2(:,:,i)*XY(:,:,i)); + end + %denom = max(1, CPD.nsamples + gamma + Z); + denom = CPD.nsamples + gamma + Z; + S = (S + gamma*eye(self_size)) / denom; + if strcmp(CPD.cov_type, 'diag') + S = diag(diag(S)); + end + CPD.cov = repmat(S, [1 1 dpsize]); + else + for i=1:dpsize + % Eqn 1 from table 2 in TR + S = YY(:,:,i) - B2(:,:,i)*XY(:,:,i); + %denom = max(1, w(i) + gamma + Z); % gives wrong answers on mhmm1 + denom = w(i) + gamma + Z; + S = (S + gamma*eye(self_size)) / denom; + CPD.cov(:,:,i) = S; + end + if strcmp(CPD.cov_type, 'diag') + for i=1:dpsize + CPD.cov(:,:,i) = diag(diag(CPD.cov(:,:,i))); + end + end + end +end + + +check_covars = 0; +min_covar = 1e-5; +if check_covars % prevent collapsing to a point + for i=1:dpsize + if min(svd(CPD.cov(:,:,i))) < min_covar + disp(['resetting singular covariance for node ' num2str(CPD.self)]); + CPD.cov(:,:,i) = CPD.init_cov(:,:,i); + end + end +end + + +