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

first hg version after svn

+function [a, b, error] = weightedRegression(x, z, w)
+% [a , b, error] = fitRegression(x, z, w);
+% % Weighted scalar linear regression
+%
+% Find a,b to minimize
+% error = sum(w * |z - (a*x + b)|^2) 
+% and x(i) is a scalar
+
+if nargin < 3, w = ones(1,length(x)); end
+
+w = w(:)';
+x = x(:)';
+z = z(:)';
+
+W = sum(w);
+Y = sum(w .* z);
+YY = sum(w .* z .* z);
+YTY = sum(w .* z .* z);
+X = sum(w .* x);
+XX = sum(w .* x .* x);
+XY = sum(w .* x .* z);
+
+[b, a] = clg_Mstep_simple(W, Y, YY, YTY, X, XX, XY);
+error = sum(w .* (z - (a*x + b)).^2 );
+
+if 0
+  % demo
+  seed = 1;
+  rand('state', seed);   randn('state', seed);
+  x = -10:10;
+  N = length(x);
+  noise = randn(1,N);
+  aTrue = rand(1,1);
+  bTrue = rand(1,1);
+  z = aTrue*x + bTrue + noise;
+  
+  w = ones(1,N);
+  [a, b, err] = weightedRegression(x, z, w);
+  
+  b2=regress(z(:), [x(:) ones(N,1)]);
+  assert(approxeq(b,b2(2)))
+  assert(approxeq(a,b2(1)))
+
+  % Make sure we go through x(15) perfectly
+  w(15) = 1000;
+  [aW, bW, errW] = weightedRegression(x, z, w);
+
+  figure;
+  plot(x, z, 'ro')
+  hold on
+  plot(x, a*x+b, 'bx-')
+  plot(x, aW*x+bW, 'gs-')
+  title(sprintf('a=%5.2f, aHat=%5.2f, aWHat=%5.3f, b=%5.2f, bHat=%5.2f, bWHat=%5.3f, err=%5.3f, errW=%5.3f', ...
+		aTrue, a, aW, bTrue, b, bW, err, errW))
+  legend('truth', 'ls', 'wls')
+  
+end
+