Related papers: Stein factors for negative binomial approximation …
One major obstacle in applications of Stein's method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the…
We give a number of results on approximations of Markov kernels in total variation and Wasserstein norms weighted by a Lyapunov function. The results are applied to examples from Bayesian statistics where approximations to transition…
In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular,…
In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…
We develop Stein's method for $\alpha$-stable approximation with $\alpha\in(0,1]$, continuing the recent line of research by Xu \cite{lihu} and Chen, Nourdin and Xu \cite{C-N-X} in the case $\alpha\in(1,2).$ The main results include an…
We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the…
Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent…
We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $L^1$ Wasserstein distance. We show that measure satisfying certain self-similarity conditions…
Bayesian optimal experimental design (OED) provides a principled framework for selecting observations or experiments. We introduce new Bayesian design criteria based on the expected Wasserstein-$p$ distance between the prior and posterior…
We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…
Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized…
We present new insights into causal inference in the context of Heterogeneous Treatment Effects by proposing natural variants of Random Forests to estimate the key conditional distributions. To achieve this, we recast Breiman's original…
This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…
We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well…
Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…
Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…