robbinsmonroalpha.m.svn-base

Bayesian Surprise Toolkit for Matlab T. Nathan Mundhenk, Laurent Itti

%ROBBINSMONROALPHA compute new alpha value for the surprise model
%   A2 = ROBBINSMONROALPHA(X,A1,B1,DECAY)
%   A2 = ROBBINSMONROALPHA(X,A1,B1,DECAY,N)
%
%   Compute a new alpha value for surprise using the Robbins-Monro style of
%   finding the maximum likelyhood value for alpha. This method works by
%   starting with the derivative of the gamma pdf with respect to alpha and
%   uses that the make measured updates to alpha in a method designed to
%   reduce the difference between the estimate of alpha and the true value
%   of alpha. 
%
%   A2 is the return new alpha value as estimated by the formula.
%
%   X is a new sample input to the formula. Note that this method is
%   recursive and works by taking in new samples one at a time. 
%
%   A1 is the current estimated value for alpha.
%
%   B1 is the current estimated value for beta. It should be noted that
%   this value can interact with the computation of a new beta value. As
%   such, if beta is estimated based on alpha, this should be an
%   independant estimate. A good estimate is the asymptotic value of beta
%   given we assume the null hypothesis is true. 
%
%   DECAY this is the decay term for the surprise model. 
%
%   N This is an estimate of N. It can be the same as B1 in many cases. As
%   such if it is uspecified, it is set to the same as B1. 
%
%   See also: newalphabeta, runsm, klgamma, graphkl, gamma, psi, digamma, eulermasch 
%
%   T. Nathan Mundhenk
%   [e-mail]

%
% //////////////////////////////////////////////////////////////////// %
% The Baysian Surprise Matlab Toolkit - Copyright (C) 2004-2007        %
% by the University of Southern California (USC) and the iLab at USC.  %
% See http://iLab.usc.edu for information about this project.          %
% //////////////////////////////////////////////////////////////////// %
% This file is part of the Baysian Surprise Matlab Toolkit             %
%                                                                      %
% The Baysian Surprise Matlab Toolkit is free software; you can        %
% redistribute it and/or modify it under the terms of the GNU General  %
% Public License as published by the Free Software Foundation; either  %
% version 2 of the License, or (at your option) any later version.     %
%                                                                      %
% The Baysian Surprise Matlab Toolkit is distributed in the hope       %
% that it will be useful, but WITHOUT ANY WARRANTY; without even the   %
% implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR      %
% PURPOSE.  See the GNU General Public License for more details.       %
%                                                                      %
% You should have received a copy of the GNU General Public License    %
% along with the iBaysian Surprise Matlab Toolkit; if not, write       %
% to the Free Software Foundation, Inc., 59 Temple Place, Suite 330,   %
% Boston, MA 02111-1307 USA.                                           %
% //////////////////////////////////////////////////////////////////// %
%
% Primary maintainer for this file: T. Nathan Mundhenk <[e-mail]>
%

function a2 = robbinsmonroalpha(x,a1,b1,decay,N)    

% This line does something for some reason. I do not know why. Let me know
% if you have any idea why it affects my algo. to remove it. 
if nargin < 5 N = b1; end

a2 = a1*decay + (log(b1) - digamma(a1*decay,1000) + log(x)) ./ N;