Related papers: Approximation rate in Wasserstein distance of prob…
The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust…
We introduce an algorithm which, given probabilities $\mu \leq_{\text{cx}} \nu$ in convex order and defined on a separable Banach space $B$, constructs finitely-supported approximations $\mu_n \to \mu, \nu_n\to \nu$ which are in convex…
Consider an empirical measure $\mathbb{P}_n$ induced by $n$ iid samples from a $d$-dimensional $K$-subgaussian distribution $\mathbb{P}$ and let $\gamma = N(0,\sigma^2 I_d)$ be the isotropic Gaussian measure. We study the speed of…
The adapted Wasserstein distance controls the calibration errors of optimal values in various stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. However, statistical aspects of the adapted…
This paper primarily considers the robust estimation problem under Wasserstein distance constraints on the parameter and noise distributions in the linear measurement model with additive noise, which can be formulated as an…
Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…
We prove the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, both with Lipschitz-continuous and with polynomial…
We establish quantitative convergence rates for stochastic particle approximation based on Nanbu-type Monte Carlo schemes applied to a broad class of collisional kinetic models. Using coupling techniques and stability estimates 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,…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
We obtain explicit $p$-Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically…
We determine the convergence speed of a numerical scheme for approximating one-dimensional continuous strong Markov processes. The scheme is based on the construction of coin tossing Markov chains whose laws can be embedded into the process…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
Let $(X_t)_{t \geq 0}$ be a diffusion process defined on a compact Riemannian manifold, and for $\alpha > 0$, let $$ \mu_t^{(\alpha)} = \frac{\alpha}{t^\alpha} \int_{0}^{t} \delta_{X_s} \, s^{\alpha - 1} \mathrm{d} s $$ be the associated…
After shortly reviewing the fundamentals of approach theory as introduced by R. Lowen in 1989, we show that this theory is intimately related with the well-known Wasserstein metric on the space of probability measures with a finite first…
Detecting tiny objects is a very challenging problem since a tiny object only contains a few pixels in size. We demonstrate that state-of-the-art detectors do not produce satisfactory results on tiny objects due to the lack of appearance…
A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
We establish various bounds on the solutions to a Stein equation for Poisson approximation in Wasserstein distance with non-linear transportation costs. The proofs are a refinement of those in [Barbour and Xia (2006)] using the results in…
A method for analyzing non-asymptotic guarantees of numerical discretizations of ergodic SDEs in Wasserstein-2 distance is presented by Sanz-Serna and Zygalakis in ``Wasserstein distance estimates for the distributions of numerical…