相关论文: Smoothed Distance Kernels for MMDs and Application…

Kernel methods are learning algorithms that enjoy solid theoretical foundations while suffering from important computational limitations. Sketching, which consists in looking for solutions among a subspace of reduced dimension, is a well…

We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…

In a high-dimensional regression framework, we study consequences of the naive two-step procedure where first the dimension of the input variables is reduced and second, the reduced input variables are used to predict the output variable…

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying…

Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the…

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a…

We reveal a precise mathematical framework about a new family of generative models which we call Gradient Flow Drifting. With this framework, we prove an equivalence between the recently proposed Drifting Model and the Wasserstein gradient…

The efficiency of a Markov sampler based on the underdamped Langevin diffusion is studied for high dimensional targets with convex and smooth potentials. We consider a classical second-order integrator which requires only one gradient…

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL)…

Distance metrics are central to machine learning, yet distances between ensembles of quantum states remain poorly understood due to fundamental quantum measurement constraints. We introduce a hierarchy of integral probability metrics,…

The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT…

The Quasi Manhattan Wasserstein Distance (QMWD) is a metric designed to quantify the dissimilarity between two matrices by combining elements of the Wasserstein Distance with specific transformations. It offers improved time and space…

Despite their advantages, normalizing flows generally suffer from several shortcomings including their tendency to generate unrealistic data (e.g., images) and their failing to detect out-of-distribution data. One reason for these…

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 are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functions belong to a reproducing-kernel space. A kernel typically…

We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…

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…

The smooth 1-Wasserstein distance (SWD) $W_1^\sigma$ was recently proposed as a means to mitigate the curse of dimensionality in empirical approximation while preserving the Wasserstein structure. Indeed, SWD exhibits parametric convergence…