General Bounds for Maximum Mean Discrepancy Statistics

The classical maximum mean discrepancy statistics, i.e., MMDb(F ,X, Y ) and MMDu(F , X, Y ), to test whether two samples X = {x1, x2, · · · , xm} and Y = {y1, y2, · · · , yn} are drawn from the different distributions p and q. MMDb and MMDu are two very useful and effective statistics of which the bounds are derived based on the assumption of m = n. This paper relaxes this assumption and provides the general bounds for these two statistics statistics MMDb and MMD 2 u. The derived results show that the traditional bounds derived in previous study are the special cases of our general bounds.