Home > freetb4matlab > info-theory > conditionalentropy_XY.m

conditionalentropy_XY

PURPOSE ^

%

SYNOPSIS ^

function val=conditionalentropy_XY(XY)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {} conditionalentropy_XY (@var{x}, @var{y}) 
%
% Computes the
% @iftex
% @tex
% $H(\frac{X}{Y}) = \sum_i{P(Y_i) H(\frac{X}{Y_i})$, where
% $H(\frac{X}{Y_i}) = \sum_k{-P(\frac{X_k}{Y_i}) \log(P(\frac{X_k}{Y_i}))$,
% where $P(\frac{X_k}{Y_i} = \frac{P(X_k,Y_i)}{P(Y_i)}$.
% @end tex
% @end iftex
% @ifinfo
% H(X/Y) = SUM( P(Yi)*H(X/Yi) ) , where 
% H(X/Yi) = SUM( -P(Xk/Yi)log(P(Xk/Yi))), where
% P(Xk/Yi) = P(Xk,Yi)/P(Yi).
% @end ifinfo
% The matrix @var{xy} must have @var{y} along rows and @var{x} along columns.
% @iftex
% @tex
% $X_i = \sum{COL_i} 
% $Y_i = \sum{ROW_i}
% $H(X|Y) = H(X,Y) - H(Y)$
% @end tex
% @end iftex
% @ifinfo
% Xi = SUM( COLi ) 
% Yi = SUM( ROWi )
% H(X|Y) = H(X,Y) - H(Y)
% @end ifinfo
% @end deftypefn
% @seealso{entropy, conditionalentropy}

CROSS-REFERENCE INFORMATION ^

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