is a test statistic for the two-sample testing problem, where acceptance or rejection decisions are made for a null hypothesis [@gretton2012]; thus, in other words, a minimum MMD enforces that two distributions, in this case that of the image $\mathbf{X}$ and that associated with the reference images ($\mathbf{S}$ for style and $\mathbf{R}$ for style) are similar enough, within a statistical relevance limit. The last work [@li2017] indicates that the relation of the neural style transfer abides to the original principle stated by Reinhard et al. [-@Reinhard:2001], namely of feature distribution matching. The neural style transfer [@Gatys:2015] implements an approximation of the exact solution, which would have been given by inverting and composing the Cumulative Density Functions (CDF).

In an attempt to accelerate the transfer, Ulyanov et al. [-@ulyanov2016] and Johnson et al. [@johnson2016] learned the inverse mapping by a deep CNN. Yet this approach has the disadvantage that only a specific reference image equivalent CDF may be learned by the CNN; another style from another reference image requires another CNN. Thus, this approximation restricts the number of transferable styles to the number of CNNs trained. The limitation was very recently approached by Huang and Belongie [-@huang2017], which assumes independent Gaussians 