Results 51 to 60 of about 32,144 (182)
Irregularity of Distribution in Wasserstein Distance [PDF]
Journal of Fourier Analysis and Applications, 2020 We study the non-uniformity of probability measures on the interval and the circle. On the interval, we identify the Wasserstein-$p$ distance with the classical $L^p$-discrepancy. We thereby derive sharp estimates in Wasserstein distances for the irregularity of distribution of sequences on the interval and the circle.
openaire +3 more sources
The Gromov–Wasserstein Distance: A Brief Overview
Axioms, 2014 We recall the construction of the Gromov–Wasserstein distance and concentrate on quantitative aspects of the definition.
Facundo Mémoli
doaj +1 more source
Basic statistics for probabilistic symbolic variables: a novel metric-based approach
, 2013 In data mining, it is usually to describe a set of individuals using some summaries (means, standard deviations, histograms, confidence intervals) that generalize individual descriptions into a typology description. In this case, data can be described by
Irpino, Antonio, Verde, Rosanna
core +1 more source
Scalar conservation laws seen as gradient flows: known results and new perspectives
ESAIM: Proceedings and Surveys, 2016 We review some results in the literature which attempted (only partly successfully) at linking the theory of scalar conservation laws with the Wasserstein gradient flow theory.
Di Francesco Marco
doaj +1 more source
Towards Inverse Modeling of Landscapes Using the Wasserstein Distance
Geophysical Research Letters, 2023 Extricating histories of uplift and erosion from landscapes is crucial for many branches of the Earth sciences. An objective way to calculate such histories is to identify calibrated models that minimize misfit between observations (e.g., topography) and
M. J. Morris, A. G. Lipp, G. G. Roberts
doaj +1 more source
High-Dimensional Distributionally Robust Mean-Variance Efficient Portfolio Selection
Mathematics, 2023 This paper introduces a novel distributionally robust mean-variance portfolio estimator based on the projection robust Wasserstein (PRW) distance. This approach addresses the issue of increasing conservatism of portfolio allocation strategies due to high-
Zhonghui Zhang, Huarui Jing, Chihwa Kao
doaj +1 more source
Advanced Intelligent Discovery, EarlyView.We investigate MACE‐MP‐0 and M3GNet, two general‐purpose machine learning potentials, in materials discovery and find that both generally yield reliable predictions. At the same time, both potentials show a bias towards overstabilizing high energy metastable states. We deduce a metric to quantify when these potentials are safe to use.
Konstantin S. Jakob +2 more
wiley +1 more source
Wasserstein distance, Fourier series and applications [PDF]
Monatshefte für Mathematik, 2021 We study the Wasserstein metric $W_p$, a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance $W_1$ between the distribution of quadratic residues in a finite field $\mathbb{F}_p$ and uniform distribution by $\lesssim p^{-1/2}$ (the ...
openaire +3 more sources
First and second moments for self-similar couplings and Wasserstein distances
, 2014 We study aspects of the Wasserstein distance in the context of self-similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of \emph{couplings}, which are measures on the product space ...
Fraser, Jonathan M.
core +1 more source
Advanced Intelligent Discovery, EarlyView.This work presents a novel generative artificial intelligence (AI) framework for inverse alloy design through operations (optimization and diffusion) within learned compact latent space from variational autoencoder (VAE). The proposed work addresses challenges of limited data, nonuniqueness solutions, and high‐dimensional spaces.
Mohammad Abu‐Mualla +4 more
wiley +1 more source