Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-
smooth Riesz kernels show a rich structure as singular measures can become absolutely …

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large
scale computations. In this paper, we show that MMD flows with Riesz kernels $ K (x, y) …

Kernel-based methods are heavily used in machine learning. However, they suffer from
complexity in the number of considered data points. In this paper, we propose an …

In inverse problems, many conditional generative models approximate the posterior
measure by minimizing a distance between the joint measure and its learned approximation …

Most commonly used $ f $-divergences of measures, eg, the Kullback-Leibler divergence,
are subject to limitations regarding the support of the involved measures. A remedy consists …

We compute the equilibrium measure in dimension d= s+ 4 associated to a Riesz s-kernel
interaction with an external field given by a power of the Euclidean norm. Our study reveals …

This paper provides results on Wasserstein gradient flows between measures on the real
line. Utilizing the isometric embedding of the Wasserstein space P 2 (R) into the Hilbert …

We give a comprehensive description of Wasserstein gradient flows of maximum mean
discrepancy (MMD) functionals $\mathcal F_\nu:=\text {MMD} _K^ 2 (\cdot,\nu) $ towards …

In this work, we study the Wasserstein gradient flow of the Riesz energy defined on the
space of probability measures. The Riesz kernels define a quadratic functional on the space …

As the problem of minimizing functionals on the Wasserstein space encompasses many
applications in machine learning, different optimization algorithms on $\mathbb {R}^ d …