function T = transferEntropyKDE(X,Y,t,w,N,bw_coeff)
% This function computes the transfer entropy between time series X and Y,
% with the flow of information directed from X to Y. Probability density
% estimation is based on Guassian kernel density estimation.
% For details, please see T Schreiber, "Measuring information transfer", Physical Review Letters, 85(2):461-464, 2000.
% X: source time series in 1-D vector
% Y: target time series in 1-D vector
% t: time lag in X from present
% w: time lag in Y from present
% N: number of equally spaced points along each dimension where probabilities are to be estimated
% bw_coeff: multiplier that adjusts the rule of thumb Gaussian bandwidth, a value of 1 means no change in the rule of thumb bandwidth
% T: transfer entropy (bits)
% Copyright 2011 Joon Lee
% This program 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 3 of the License, or
% (at your option) any later version.
% This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
% fix block lengths at 1
% go through the time series X and Y, and populate Xpat, Ypat, and Yt
Xpat=; Ypat=; Yt=;
for i=max([l+t k+w]):1:min([length(X) length(Y)])
% compute transfer entropy
pdf(i,j,k)=mdKDE([Xpat Ypat Yt],[Xpati(i) Ypati(j) Yti(k)],bw_coeff);
pdf=pdf./sum(sum(sum(pdf))); % normalize