Related papers: Approximation rate in Wasserstein distance of prob…
This paper studies convergence of empirical measures smoothed by a Gaussian kernel. Specifically, consider approximating $P\ast\mathcal{N}_\sigma$, for $\mathcal{N}_\sigma\triangleq\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$, by…
Self-supervised sequential recommendation significantly improves recommendation performance by maximizing mutual information with well-designed data augmentations. However, the mutual information estimation is based on the calculation of…
This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
For martingales with a wide range of integrability, we will quantify the rate of convergence of the central limit theorem via Wasserstein distances of order $r$, $1\le r\le 3$. Our bounds are in terms of Lyapunov's coefficients and the…
Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…
The Wasserstein distance provides a notion of dissimilarities between probability measures, which has recent applications in learning of structured data with varying size such as images and text documents. In this work, we study the…
Estimating the rate of convergence of the empirical measure of an i.i.d. sample to the reference measure is a classical problem in probability theory. Extending recent results of Ambrosio, Stra and Trevisan on 2-dimensional manifolds, in…
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any…
Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
Von Renesse and the author (Ann. Prob. '09) developed a second order calculus on the Wasserstein space P([0,1]) of probability measures on the unit interval. The basic objects of interest had been Dirichlet form, semigroup and continuous…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
For a class of (non-symmetric) diffusion processes on a length space, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold, the exact convergence rate is derived for $({\mathbb E}…
We estimate rates of convergence for empirical measures associated with the subordinated fractional Brownian motion to the uniform distribution on the flat torus under the Wasserstein distance $\mathbb{W}_p$ for all $p\geq1$. In particular,…
In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…
Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing under $L_1$-distance. However, when the support is very large or even continuous,…
This paper studies sampling error bounds for denoising diffusion probabilistic models (DDPMs) in the 2-Wasserstein distance. Our contributions are threefold. (i) Under general Lipschitz-type conditions on the score function and for a broad…