Related papers: Maximum Mean Discrepancy Gradient Flow
This paper is motivated by addressing open questions in distributionally robust chance-constrained programs (DRCCP) using the popular Wasserstein ambiguity sets. Specifically, the computational techniques for those programs typically place…
The Maximum Mean Discrepancy (MMD) has found numerous applications in statistics and machine learning, most recently as a penalty in the Wasserstein Auto-Encoder (WAE). In this paper we compute closed-form expressions for estimating the…
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to an absolutely continuous curve on the $2$-Wasserstein…
We study the convergence of gradient flow for the training of deep neural networks. If Residual Neural Networks are a popular example of very deep architectures, their training constitutes a challenging optimization problem due notably to…
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…
This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…
Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a…
Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Among dissimilarities between probability distributions, the Kernel Stein Discrepancy (KSD) has received much interest recently. We investigate the properties of its Wasserstein gradient flow to approximate a target probability distribution…
Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…
We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a new connection between neural tangent kernel (NTK) and MMD. This connection enables us to develop a computationally efficient and memory-efficient…
We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We…
Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
Generative models have been successfully used for generating realistic signals. Because the likelihood function is typically intractable in most of these models, the common practice is to use "implicit" models that avoid likelihood…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
In this paper, we propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs). From a perspective of physical simulation, we redefine the problem of approximating the gradient flow utilizing…