comparison toolboxes/FullBNT-1.0.7/KPMstats/mixgauss_Mstep.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [mu, Sigma] = mixgauss_Mstep(w, Y, YY, YTY, varargin)
+% MSTEP_COND_GAUSS Compute MLEs for mixture of Gaussians given expected sufficient statistics
+% function [mu, Sigma] = Mstep_cond_gauss(w, Y, YY, YTY, varargin)
+%
+% We assume P(Y|Q=i) = N(Y; mu_i, Sigma_i)
+% and w(i,t) = p(Q(t)=i|y(t)) = posterior responsibility
+% See www.ai.mit.edu/~murphyk/Papers/learncg.pdf.
+%
+% INPUTS:
+% w(i) = sum_t w(i,t) = responsibilities for each mixture component
+%  If there is only one mixture component (i.e., Q does not exist),
+%  then w(i) = N = nsamples,  and 
+%  all references to i can be replaced by 1.
+% YY(:,:,i) = sum_t w(i,t) y(:,t) y(:,t)' = weighted outer product
+% Y(:,i) = sum_t w(i,t) y(:,t) = weighted observations
+% YTY(i) = sum_t w(i,t) y(:,t)' y(:,t) = weighted inner product
+%   You only need to pass in YTY if Sigma is to be estimated as spherical.
+%
+% Optional parameters may be passed as 'param_name', param_value pairs.
+% Parameter names are shown below; default values in [] - if none, argument is mandatory.
+%
+% 'cov_type' - 'full', 'diag' or 'spherical' ['full']
+% 'tied_cov' - 1 (Sigma) or 0 (Sigma_i) [0]
+% 'clamped_cov' - pass in clamped value, or [] if unclamped [ [] ]
+% 'clamped_mean' - pass in clamped value, or [] if unclamped [ [] ]
+% 'cov_prior' - Lambda_i, added to YY(:,:,i) [0.01*eye(d,d,Q)]
+%
+% If covariance is tied, Sigma has size d*d.
+% But diagonal and spherical covariances are represented in full size.
+
+[cov_type, tied_cov,  clamped_cov, clamped_mean, cov_prior, other] = ...
+    process_options(varargin,...
+		    'cov_type', 'full', 'tied_cov', 0,  'clamped_cov', [], 'clamped_mean', [], ...
+		    'cov_prior', []);
+
+[Ysz Q] = size(Y);
+N = sum(w);
+if isempty(cov_prior)
+  %cov_prior = zeros(Ysz, Ysz, Q);
+  %for q=1:Q
+  %  cov_prior(:,:,q) = 0.01*cov(Y(:,q)');
+  %end
+  cov_prior = repmat(0.01*eye(Ysz,Ysz), [1 1 Q]);
+end
+%YY = reshape(YY, [Ysz Ysz Q]) + cov_prior; % regularize the scatter matrix
+YY = reshape(YY, [Ysz Ysz Q]);
+
+% Set any zero weights to one before dividing
+% This is valid because w(i)=0 => Y(:,i)=0, etc
+w = w + (w==0);
+		    
+if ~isempty(clamped_mean)
+  mu = clamped_mean;
+else
+  % eqn 6
+  %mu = Y ./ repmat(w(:)', [Ysz 1]);% Y may have a funny size
+  mu = zeros(Ysz, Q);
+  for i=1:Q
+    mu(:,i) = Y(:,i) / w(i);
+  end
+end
+
+if ~isempty(clamped_cov)
+  Sigma = clamped_cov;
+  return;
+end
+
+if ~tied_cov
+  Sigma = zeros(Ysz,Ysz,Q);
+  for i=1:Q
+    if cov_type(1) == 's'
+      % eqn 17
+      s2 = (1/Ysz)*( (YTY(i)/w(i)) - mu(:,i)'*mu(:,i) );
+      Sigma(:,:,i) = s2 * eye(Ysz);
+    else
+      % eqn 12
+      SS = YY(:,:,i)/w(i)  - mu(:,i)*mu(:,i)';
+      if cov_type(1)=='d'
+	SS = diag(diag(SS));
+      end
+      Sigma(:,:,i) = SS;
+    end
+  end
+else % tied cov
+  if cov_type(1) == 's'
+    % eqn 19
+    s2 = (1/(N*Ysz))*(sum(YTY,2) + sum(diag(mu'*mu) .* w));
+    Sigma = s2*eye(Ysz);
+  else
+    SS = zeros(Ysz, Ysz);
+    % eqn 15
+    for i=1:Q % probably could vectorize this...
+      SS = SS + YY(:,:,i)/N - mu(:,i)*mu(:,i)';
+    end
+    if cov_type(1) == 'd'
+      Sigma = diag(diag(SS));
+    else
+      Sigma = SS;
+    end
+  end
+end
+
+if tied_cov
+  Sigma =  repmat(Sigma, [1 1 Q]);
+end
+Sigma = Sigma + cov_prior;