Related papers: Localization and dimension free estimates for maxi…
We discuss a one-sample location test that can be used in the case of high-dimensional data. For high-dimensional data, the power of Hotelling's test decrises when the dimension is close to the sample size. To address this loss of power,…
Exploiting the properties of the Jost-Lehmann-Dyson representation, it is shown that in 1+2 or more spacetime dimensions, a nonempty smallest localization region can be associated with each local observable (except for the c-numbers) in a…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. The Dyck and Motzkin shifts are well-known examples of transitive subshifts over a finite alphabet that are not…
In this note, we study maximizers for Fourier extension inequalities on the sphere. We prove that constant functions are local maximizers for the $L^p(\mathbb{S}^{d-1})$ to $L^p(\mathbb{R}^d)$ Fourier extension estimates in the same range…
Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…
Loss functions is a crucial factor that affecting the detection precision in object detection task. In this paper, we optimize both two loss functions for classification and localization simultaneously. Firstly, by multiplying an IoU-based…
Statistical depth functions provide measures of the outlyingness, or centrality, of the elements of a space with respect to a distribution. It is a nonparametric concept applicable to spaces of any dimension, for instance, multivariate and…
A procedure to construct symmetry-adapted Wannier functions in the framework of the maximally-localized Wannier function approach[Marzari and Vanderbilt, Phys. Rev. B \textbf{56}, 12847 (1997); Souza, Marzari, and Vanderbilt, \textit{ibid.}…
We present a new methodology and accompanying theory to test for separability of spatio-temporal functional data. In spatio-temporal statistics, separability is a common simplifying assumption concerning the covariance structure which, if…
Localization properties for Schr\"odinger means are studied in dimension higher than one.
We propose novel optimal designs for longitudinal data for the common situation where the resources for longitudinal data collection are limited, by determining the optimal locations in time where measurements should be taken. As for all…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and machine learning. A fundamental role in their numerical…
Suppose $X$ is an $\rm{RCD}(K,N)$ space with $K \in \mathbb{R}$ and $N \in (1,\infty)$. We obtain a characterisation of the Newtonian-Sobolev space $N^{1,2}(X)$ in terms of a quantity which measures to what extent a function is locally…
Recent years have seen great progress in the approximability of fundamental clustering and facility location problems on high-dimensional Euclidean spaces, including $k$-Means and $k$-Median. While they admit strictly better approximation…
We prove a uniform upper and lower bound for Delannoy numbers. This is achieved by using the representation of Delannoy numbers as the number of lattice points in high-dimensional cross-polytopes (also known as hyper-octahedrons or $\ell^1$…
In this note two results are established for energy functionals that are given by the integral of $ W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$,…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…
Space-filling experimental designs are widely used in engineering computer experiments, where only a limited number of expensive model evaluations can be afforded. Distance-based designs such as Maximin or Minimax ensure global…