Weighted sampling without replacement

Question

I have a population p of indices and corresponding weights in vector w. I want to get k samples from this population without repla

Answer 1

If you want to select a large fraction of the columns (i.e., k is not very much smaller than n), or if the weights are very skewed, you can use this refinement of Jeff's solution, which ensures that each call to randsample produces samples distinct from the previous ones.

Moreover, it returns the samples in the order in which true sampling without replacement would return them, rather than sorted.

function I=randsample_noreplace(n,k,w)
I = randsample(n, k, true, w);
while 1
    [II, idx] = sort(I);
    Idup = [false, diff(II)==0];
    if ~any(Idup)
        break
    else
        w(I) = 0;            %% Don't replace samples
        Idup (idx) = Idup;   %% find duplicates in original list
        I = [I(~Idup),  (randsample(n, sum(Idup), true, w))];
    end
end

When selecting 29 out of 30 values with uniform weights (the case that gives least benefit), it takes 3 or 4 iterations, compared with 26 without the additional line. If the weights are chosen uniformly, it still takes 3 to 5 iterations compared with around 80 without the additional line.

Also, the number of iterations is bounded by k, however skewed the distribution is.