  In this paper, we bound the error induced by using a weighted skeletonization
of two data sets for computing a two sample test with kernel maximum mean
discrepancy. The error is quantified in terms of the speed in which heat
diffuses from those points to the rest of the data, as well as how at the
weights on the reference points are, and gives a non-asymptotic,
non-probabilistic bound. The result ties into the problem of the eigenvector
triple product, which appears in a number of important problems. The error
bound also suggests an optimization scheme for choosing the best set of
reference points and weights. The method is tested on a several two sample test
examples.
