In the density estimation model, we investigate the problem of constructing adaptive honest confidence sets with diameter measured in Wasserstein distance Wp, p >=1, and for densities with unknown regularity measured on a Besov scale. As sampling domains, we focus on the d-dimensional torus Td, in which case 1
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [10] for mixtures of gaussian measures to other mixtures. We first prove in a general setting that for a set of at...
In this paper, we give estimates of the quadratic transportation cost in the conditional central limit theorem for a large class of dependent sequences. Applications to irreducible Markov chains, dynamical systems generated by intermittent maps and τ-mixing sequences are given.
We deal with Mckean-Vlasov and Boltzmann type jump equations. This means that the coefficients of the stochastic equation depend on the law of the solution, and the equation is driven by a Poisson point measure with intensity measure which depends on the law of the solution as well. In [3], Alfonsi and Bally have proved that under some suitable con...
The Gromov-Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures living on Euclidean spaces of different dimensions. In this paper, we focus on the Gromov-Wasserstein distanc...
Remote sensing observations from satellites and global biogeochemical models have combined to revolutionize the study of ocean biogeochemical cycling, but comparing the two data streams to each other and across time remains challenging due to the strong spatial-temporal structuring of the ocean. Here, we show that the Wasserstein distance provides ...
The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will help to choose between two or more priors in a given situation. To this end a new approach, the Wasserstein I...
Modern data analysis provides scientists with statistical and machine learning algorithmswith impressive performance. In front of their extensive use to tackle problems of constantlygrowing complexity, there is a real need to understand the conditions under which algorithmsare successful or bound to fail. An additional objective is to gain insights...
Published in Polymers
In this study, the effects of a hybrid filler composed of zero-dimensional spherical AlN particles and two-dimensional BN flakes on the thermal conductivity of epoxy resin were studied. The thermal conductivity (TC) of the pristine epoxy matrix (EP) was 0.22 W/(m K), while the composite showed the TC of 10.18 W/(m K) at the 75 wt% AlN-BN hybrid fil...
Published in Quantum Science & Technology
Quantifying how far the output of a learning algorithm is from its target is an essential task in machine learning. However, in quantum settings, the loss landscapes of commonly used distance metrics often produce undesirable outcomes such as poor local minima and exponentially decaying gradients. To overcome these obstacles, we consider here the r...
