MMD's y_mapping is not convenient

[thibaultdvx]

Problem
I would like to use Maximum Mean Discrepancy metric with a kernel (e.g. gaussian kernel).

According to the reference paper, we have (eq. 3):

$${{MMD}}^2 = \frac{1}{m(m-1)} \sum_{i=1}^m \sum_{j\neq i}^m k(x_i, x_j) + \frac{1}{n(n-1)} \sum_{i=1}^n \sum_{j\neq i}^n k(y_i, y_j) - \frac{2}{mn} \sum_{i=1}^m \sum_{j=1}^n k(x_i, y_j)$$

with: $k(x,y) = <\phi(x),\phi(y)>$, $k$ being a kernel and $\phi$ a transformation.

It seems to me that in your implementation, you use the form with $\phi$ (which corresponds to y_mapping) rather than using the form with a kernel.

Suggested solution
As you mentioned in the docs, MMD is a "kernel-based method", so I would suggest to use the kernel form and replace the y_mapping argument with a kernel argument. It would be more consistent with common MMD implementations I found ([1], [2], [3] or [4]).

I would be happy to make the changes if you agree!