bootstrap a dataset in Matlab for Ensemble Learning

Question

I have two matrices X (122 x 125973) and Y (1 x 125973). I want to do bootstrapping on my dataset in which I want to create B observations (say B = 3). As I understand it, the observations of size B should be randomly drawn with replacement. How can I split in the same way X and Y into smaller observation bootstrap samples?

Answer 1

randi() gives you the ability to drawn pseudorandom integers, including duplicate entries. These can then be used as indices to your observations. Thus:

X = rand(122,125973);
Y = rand(1,125973);
m = 3; % Your desired number of observations; maximum 125973
idx = randi(numel(Y),m,1) % Generate an mx1 vector
BX = X(:,idx); % 122xm matrix
BY = Y(:,idx);  % 1xm matrix

You can remove entries from X and Y as well, but since you said duplicate entries are explicitly allowed its usage may not be relevant:

X(:,idx) = [];  % [] sets to empty array, thus removes the entry

If you want multiple times m observations, simply loop over it:

N = 100;  % Number of observation matrices to be generated
m = 3; % Number of observations per matrix
X = rand(122,125973);
Y = rand(1,125973);
BX = rand(size(X,1),m,N);  % 3D matrix for collection
BY = rand(size(X,1),m,N);

for ii = 1:N  % Loop over all matrices to be generated
    idx = randi(numel(Y),m,1) % Generate an mx1 vector
    BX(:,:,ii) = X(:, idx); % 122xmxN matrix
    BY(:,:,ii) = Y(:, idx);  % 1xmxN matrix
end

BX and BY are now 3D matrices containing N matrices with m observations each. Calling BX(:,:,n) selects the nthe matrix with observations. For reading on various indexing ways I suggest to read this post.