Related papers: Low-Rate, Low-Distortion Compression with Wasserst…
A new least squares mean of positive definite matrices for the divergence associated with the sandwiched quasi-relative entropy has been introduced. It generalizes the well-known Wasserstein mean for covariance matrices of Gaussian…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
We investigate the stability of the Wasserstein distance, a metric structure on the space of probability measures arising from the theory of optimal transport, under metric ultralimits. We first show that if $(X_{i},d_{i})_{i\in\mathbb{N}}$…
We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability…
This paper is concerned with the lossy compression of general random variables, specifically with rate-distortion theory and quantization of random variables taking values in general measurable spaces such as, e.g., manifolds and fractal…
Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, and as such have a wide range of applications ranging from economics to statistics and computer science. When the marginal probability…
The nascent field of Rate-Distortion-Perception (RDP) theory is seeing a surge of research interest due to the application of machine learning techniques in the area of lossy compression. The information RDP function characterizes the…
We demonstrate that the Wasserstein distance $W_{1}$ corresponding to optical tomograms of nonclassical states faithfully captures changes that arise due to photon addition to, or subtraction from, these states. $W_{1}$ is a true measure of…
Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…
Distributed consensus in the Wasserstein metric space of probability measures on the real line is introduced in this work. Convergence of each agent's measure to a common measure is proven under a weak network connectivity condition. The…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
Let $\mu$ be a doubling measure in $\mathbb{R}^n$. We investigate quantitative relations between the rectifiability of $\mu$ and its distance to flat measures. More precisely, for $x$ in the support $\Sigma$ of $\mu$ and $r > 0$, we…
In recent years, the compression of large language models (LLMs) has emerged as a key problem in facilitating LLM deployment on resource-limited devices, reducing compute costs, and mitigating the environmental footprint due to large-scale…
Optimal transport and the Wasserstein distance $\mathcal{W}_p$ have recently seen a number of applications in the fields of statistics, machine learning, data science, and the physical sciences. These applications are however severely…
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the…
In many quantization problems, the distortion function is given by the Euclidean metric to measure the distance of a source sample to any given reproduction point of the quantizer. We will in this work regard distortion functions, which are…
The success of autoregressive models largely depends on the effectiveness of vector quantization, a technique that discretizes continuous features by mapping them to the nearest code vectors within a learnable codebook. Two critical issues…
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…