Related papers: Partial Gromov-Wasserstein Metric
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…
Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to…
Gravitational wave (GW) observations are expected to serve as a powerful and independent probe of the expansion history of the universe. By providing direct and calibration-free measurements of luminosity distances through waveform…
This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems of wave propagation, scattering and radiation for structures which include open (dielectric) waveguides, waveguide junctions, as well as…
$GW$ is an accurate method for computing electron addition and removal energies of molecules and solids. In a conventional $GW$ implementation, however, its computational cost is $O(N^4)$ in the system size $N$, which prohibits its…
The measurement of the speed of gravitational waves (GWs) is useful to distinguish general relativity from massive gravity. We propose a new model-independent strategy to measure the speed of GWs with the distorted pulsars. Theoretically,…
Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to…
First-order phase transitions in the early universe can generate stochastic gravitational waves (GWs), offering a unique probe of high-scale particle physics. The Left-Right Symmetric Model (LRSM), which restores parity symmetry at high…
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…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
For each given $p\in[1,\infty]$ we investigate certain sub-family $\mathcal{M}_p$ of the collection of all compact metric spaces $\mathcal{M}$ which are characterized by the satisfaction of a strengthened form of the triangle inequality…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We…
The space of metric measure spaces (complete separable metric spaces with a probability measure) is becoming more and more important as state space for stochastic processes. Of particular interest is the subspace of (continuum) metric…
Gravitational Wave (GW) data bring an exceptional avenue to test the underlying models of coalescing compact objects. In the regime of strong gravity and high curvature, they allow the exploration of minute deviations from the best-fit…
This note gives a self-contained overview of some important properties of the Gromov-Wasserstein (GW) distance, compared with the standard linear optimal transport (OT) framework. More specifically, I explore the following questions: are GW…