[Octave-cvsupdate] SF.net SVN: octave:[10604] trunk/octave-forge/main/statistics/inst/ regress_gp.m

[<jpi...@us...>]

Revision: 10604
          http://octave.svn.sourceforge.net/octave/?rev=10604&view=rev
Author:   jpicarbajal
Date:     2012-06-08 18:43:09 +0000 (Fri, 08 Jun 2012)
Log Message:
-----------
statistics: Adding explanation ofr the difference between the formulas in the book GPML and the one sin the function.

Modified Paths:
--------------
    trunk/octave-forge/main/statistics/inst/regress_gp.m

Modified: trunk/octave-forge/main/statistics/inst/regress_gp.m
===================================================================
--- trunk/octave-forge/main/statistics/inst/regress_gp.m	2012-06-08 18:39:56 UTC (rev 10603)
+++ trunk/octave-forge/main/statistics/inst/regress_gp.m	2012-06-08 18:43:09 UTC (rev 10604)
@@ -46,6 +46,19 @@
 
   x  = [ones(1,size(x,1)); x'];
 
+  ## Juan Pablo Carbajal <car...@if...>
+  ## Note that in the book the equation (below 2.11) for the A reads
+  ## A  = (1/sy^2)*x*x' + inv (Vp);
+  ## where sy is the scalar variance of the of the residuals (i.e y = x' * w + epsilon)
+  ## and epsilon is drawn from N(0,sy^2). Vp is the variance of the parameters w.
+  ## Note that
+  ## (sy^2 * A)^{-1} = (1/sy^2)*A^{-1} =  (x*x' + sy^2 * inv(Vp))^{-1};
+  ## and that the formula for the w mean is
+  ## (1/sy^2)*A^{-1}*x*y
+  ## Then one obtains
+  ## inv(x*x' + sy^2 * inv(Vp))*x*y
+  ## Looking at the formula bloew we see that Sp = (1/sy^2)*Vp
+  ## making the regression depend on only one parameter, Sp, and not two.
   A  = x*x' + inv (Sp);
   K  = inv (A);
   wm = K*x*y;

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