MMD's `y_mapping` is not convenient

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!

Begin at the Maximum Mean Discrepancy section in MONAI's metrics documentation and read the linked reference paper to understand the requested kernel form. Trace the implementation and any callers from that entry point; done means the API supports a kernel argument consistently with the documented MMD equation.