MutualInfo.m

function [MI] = MutualInfo(CountsMat)
%MutualInfo calculates the mutual information between Y and {X1,...XN}.
%   [MI] = MutualInfo(CountsMat) is the mutual information between the Y
%   variable and the X variables considered as one vector valued variable
%   {X1, ... XN}.
%
%   Inputs
%
%   CountsMat: An array that contains the counts (or joint probability 
%   values) of the various states of the variables. The first index 
%   corresponds to the state of the Y variable. The second through N+1 
%   indexes correspond to the states of the X1 to XN variables. 
%
%   Outputs
%
%   MI: The mutual information between Y and {X1, ... XN} in bits.
%
%
%       Version 2.0

% Version Information
%
%   1.0: 10/6/11 - The original version of the program was created before
%   and modified up to this data. (Nick Timme)
%
%   2.0: 3/20/13 - The formatting of the program was modified for inclusion
%   in the toolbox. (Nick Timme)
%

%==============================================================================
% Copyright (c) 2013, The Trustees of Indiana University
% All rights reserved.
% 
% Authors: Nick Timme (nmtimme@umail.iu.edu)
% 
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
% 
%   1. Redistributions of source code must retain the above copyright notice,
%      this list of conditions and the following disclaimer.
% 
%   2. Redistributions in binary form must reproduce the above copyright notice,
%      this list of conditions and the following disclaimer in the documentation
%      and/or other materials provided with the distribution.
% 
%   3. Neither the name of Indiana University nor the names of its contributors
%      may be used to endorse or promote products derived from this software
%      without specific prior written permission.
% 
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
% POSSIBILITY OF SUCH DAMAGE.
%==========================================================================

% Obtain the number of states for each variable
nS = size(CountsMat);

% Obtain the number of X variables
N = length(nS) - 1;

% Convert the CountsMat to a joint probability distribution. (Note, this
% will have no effect if the CountsMat is already the joint probability
% distribution.)
Pxy = CountsMat/sum(CountsMat(:));

% Find the joint probabilities for the Y and {X1,...XN} variables
Px = repmat(sum(Pxy,1),[nS(1),ones([1,N])]);
Py = repmat(sum(Pxy(:,:),2),[1,nS(2:end)]);

% Calculate the mutual information
temp = Pxy.*log2(Pxy./(Px.*Py));

% Matlab incorrectly gives states with Pxy = 0 a non-finite value. 
temp(~isfinite(temp)) = 0;

% Sum over the terms to get the mutual information
MI = sum(temp(:));



end