Related papers: New error bounds in multivariate normal approximat…
We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\partial M$ to some reference measure, under the quadratic Wasserstein…
We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide…
We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds…
Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this…
We prove the large-dimensional Gaussian approximation of a sum of $n$ independent random vectors in $\mathbb{R}^d$ together with fourth-moment error bounds on convex sets and Euclidean balls. We show that compared with classical…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
We obtain explicit Berry-Esseen bounds in the Kolmogorov distance for the normal approximation of non-linear functionals of vectors of independent random variables. Our results are based on the use of Stein's method and of random difference…
The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
We construct a continuous family of exchangeable pairs by perturbing the random variable through diffusion processes on manifold in order to apply Stein method to certain geometric settings. We compare our perturbation by diffusion method…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\eta$. Motivated by problems in signal processing and…
We derive a new result for exponential approximation using Stein's method of exchangeable pairs. As an application, an exponential limit theorem with error term is derived for |Tr(U)|^2, where Tr(U) denotes the trace of a matrix chosen from…
In this paper, we prove that the time supremum of the Wasserstein distance between the time-marginals of a uniformly elliptic multidimensional diffusion with coefficients bounded together with their derivatives up to the order $2$ in the…
We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable. In the case of deterministic and non-negative integrands,…
We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…