fof-visually-guided/elutils/+stats/mutual_information.m

function mi = mutual_information(X,Y,binwidth)
% mi = mutual_information(x,y)
% X and Y are two discrete variables of the same size.

% if variables are cateogircal or cell, turn into numeric.
if iscell(X)
    X = categorical(X);
end
if iscategorical(X)
    X = double(X);
end
if iscell(Y)
    Y = categorical(Y);
end
if iscategorical(Y)
    Y = double(Y);
end
% the joint entropy of X and Y
hxy = histcounts2(X,Y,'BinWidth',binwidth);
pxy = hxy(:)./sum(hxy(:));
pxy(pxy==0) = 1e-100; 
entropy_XY = sum(pxy.*log(pxy));


% the entropy of X
hx = histcounts(X,'BinWidth',binwidth);
px = hx./sum(hx); %probability distribution 
px(px==0) = 1e-100; % to avoid error in log calculation
entropy_X = sum(px .* log(px));
% the entropy of Y
hy = histcounts(Y,'BinWidth',binwidth);
py = hy./sum(hy); %probability distribution 
py(py==0) = 1e-100; % to avoid error in log calculation
entropy_Y = sum(py .* log(py));

% mutual information
mi = entropy_X + entropy_Y - entropy_XY;
end