mirror of https://github.com/jlizier/jidt
73 lines
2.4 KiB
Matlab
Executable File
73 lines
2.4 KiB
Matlab
Executable File
% function conditionalmutualinformationempirical(xn,yn,zn)
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%
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% Computes the mutual information over all samples xn of a random
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% variable X with samples yn of a random variable Y, conditioning on
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% samples zn of a random variable Z.
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%
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% Inputs:
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% - xn - matrix of samples of outcomes x. May be a 1D vector of samples, or
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% a 2D matrix, where each row is a vector sample for a multivariate X.
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% - yn - matrix of samples of outcomes y. May be a 1D vector of samples, or
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% a 2D matrix, where each row is a vector sample for a multivariate Y.
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% Must have the same number of rows as X.
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% - zn - matrix of samples of outcomes z. May be a 1D vector of samples, or
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% a 2D matrix, where each row is a vector sample for a multivariate Z
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% which will be conditioned on.
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% Must have the same number of rows as X.
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%
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% Outputs:
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% - result - conditional mutual information of X with Y, given Z
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%
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% Copyright (C) 2017, Joseph T. Lizier
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% Distributed under GNU General Public License v3
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%
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function result = conditionalmutualinformationempirical(xn,yn,zn)
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% Should we check any potential error conditions on the input?
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if (isvector(xn))
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% Convert it to column vector if not already:
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if (size(xn,1) == 1)
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% xn has only one row:
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xn = xn'; % Transpose it so it is only column
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end
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end
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if (isvector(yn))
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% Convert it to column vector if not already:
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if (size(yn,1) == 1)
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% yn has only one row:
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yn = yn'; % Transpose it so it is only column
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end
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end
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if (isvector(zn))
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% Convert it to column vector if not already:
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if (size(zn,1) == 1)
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% zn has only one row:
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zn = zn'; % Transpose it so it is only column
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end
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end
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% Check that their number of rows are the same:
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assert(size(xn,1) == size(yn,1));
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assert(size(xn,1) == size(zn,1));
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% We need to compute H(X|Z) + H(Y|Z) - H(X,Y|Z):
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% 1. conditional joint entropy:
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H_XY_given_Z = conditionalentropyempirical([xn, yn], zn);
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% 2. conditional entropy of Y:
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H_Y_given_Z = conditionalentropyempirical(yn, zn);
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% 3. conditional entropy of X:
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H_X_given_Z = conditionalentropyempirical(xn, zn);
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result = H_X_given_Z + H_Y_given_Z - H_XY_given_Z;
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% Alternatively, note that we could compute I(X;Y,Z) - I(X;Z)
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% 1. joint MI:
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% I_X_YZ = mutualinformationempirical(xn, [yn, zn]);
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% 2. MI just from Z:
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% I_X_Z = mutualinformationempirical(xn, zn);
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% Then:
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% result = I_X_YZ - I_X_Z;
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end
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