Difference between individual and cumulative oobMargin of TreeBagger

Why aren't the following two plots the same?

b = TreeBagger(500,X,Y,'oobpred','on');
mc = oobMargin(b,'mode','cumulative');
mi = oobMargin(b,'mode','individual');
figure; plot(mc.')
figure; plot(bsxfun(@rdivide,cumsum(mi.'),(1:500).'))

[Andrew Newell]

This has my vote for best title of the week!

Answer 1

[Ilya]

When you ask for an OOB margin from one tree, you get zero if this observation was in bag for this tree. The margin is undefined in this case, and TreeBagger returns 0 by default. The cumulative calculation averages over trees for which this observation was out of bag only. Check this out:

>> load fisheriris

>> b = TreeBagger(10,meas,species,'oobpred','on');

>> mi = oobMargin(b,'mode','individual');

>> mi(1,:)

ans = 1 0 0 0 1 0 1 1 0 0

>> b.OOBIndices(1,:)

ans = 1 0 0 0 1 0 1 1 0 0

>> mc = oobMargin(b,'mode','cumulative');

>> mc(1,:)

ans = 1 1 1 1 1 1 1 1 1 1

[K]

Thank you Ilya. Not including the in-bag samples is the key.

Answer 2

[K]

Code using the individual mode that produces the same plot as the cumulative mode is the following.

load ionosphere
b = TreeBagger(500,X,Y,'oobpred','on');
mc = oobMargin(b,'mode','cumulative');
mi = oobMargin(b,'mode','individual');
figure; plot(mc.')
% figure; plot(bsxfun(@rdivide,cumsum(mi.'),(1:500).'))

cumavg = zeros(size(mc));
cumavg(:,1) = mi(:,1);
for ii = 1:size(mc,1)
    for jj = 2:size(mc,2)
        if sum(b.OOBIndices(ii,1:jj)) == 0
            cumavg(ii,jj) = mi(ii,1);
        else
            micurrent = mi(ii,1:jj);
            cumavg(ii,jj) = mean(micurrent(b.OOBIndices(ii,1:jj)));
        end
    end
end
figure; plot(cumavg.')