Missing coefficient for cross term in MMD

[nik-sm]

Apologies if I'm missing something obvious, but the estimate defined in equation (3) of https://www.jmlr.org/papers/volume13/gretton12a/gretton12a.pdf looks slightly different to the MMD estimate implemented here.

The first term makes sense to me, and subtracting m accounts for the summation over i != j (since diagonal of RBF kernel will add to m). Likewise for second term.
However the third term seems to be missing a factor 1 / (m*n).

opt-mmd/two_sample/mmd.py

Lines 44 to 49 in 5c02a92

	m = K_XX.shape[0]
	n = K_YY.shape[0]
	mmd2 = ((K_XX.sum() - m) / (m * (m - 1))
	+ (K_YY.sum() - n) / (n * (n - 1))
	- 2 * K_XY.mean())

Is this implementation intended to match the estimate linked above?

Cheers