function KLD = kld(p1,p2,type,varargin)
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%
% kld An estimate of the KL-Divergence between two density estimates
%
% kld(P,Q) estimates the KL-divergence D(P || Q) from sampling P and
% evaluating at P and Q.
% Optional Arguments:
% kld(P,Q,'type') where 'type' is one of
% 'rs','lln': (default) use the evaluation of Q at the means of P
% 'rand',N : use a stochastic approximation with N samples
% 'unscent' : use an unscented transform (deterministic) approximation
%
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% Copyright (C) 2003 Alexander Ihler; distributable under GPL -- see README.txt
% Discontinued (bad estimate, replaced by ISE for the only application)
% 'abs' : use the absolute log ratio of P & Q eval'd at P's means
if (nargin < 3) type = 'rs'; end;
switch (type),
case {'rs','lln'}, KLD = evalAvgLogL(p1,p1) - evalAvgLogL(p2,p1);
case 'rand', N = varargin{1};
ptsE = sample(p1,N); pE = kde(ptsE,1);
KLD = evalAvgLogL(p1,pE) - evalAvgLogL(p2,pE);
case 'unscent',
D = getDim(p1); N = getNpts(p1);
ptsE = getPoints(p1); wts = getWeights(p1);
ptsE = repmat(ptsE,[1,2*D+1]); % make 2*dim copies of each point
wts = repmat(wts,[1,2*D+1]); % (and its weight)
bw = getBW(p1,1:N);
for i=1:D
ptsE(i,(i-1)*N+(1:N)) = ptsE(i,(i-1)*N+(1:N)) + bw(i,:);
ptsE(i,(2*i-1)*N+(1:N)) = ptsE(i,(2*i-1)*N+(1:N)) - bw(i,:);
end;
pE = kde(ptsE,1,wts);
KLD = evalAvgLogL(p1,pE) - evalAvgLogL(p2,pE);
case 'dist', error('Distance based estimate not yet implemented');
otherwise, error('Unknown KL-divergence ''type'' argument');
end;