Related papers: On the expected L2-discrepancy of stratified sampl…
For the L_2-orthogonal projector P onto spaces of linear splines over simplicial partitions of polyhedral domains in R^d, d>1, we show that the L_infty norm of P cannot be bounded uniformly with respect to the partition. This is in contrast…
Nonparametric partitioning-based least squares regression is an important tool in empirical work. Common examples include regressions based on splines, wavelets, and piecewise polynomials. This article discusses the main methodological and…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
Given a set $P$ of $n$ points in the plane, its separability is the minimum number of lines needed to separate all its pairs of points from each other. We show that the minimum number of lines needed to separate $n$ points, picked randomly…
We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics.…
We study the asymptotics in $L^2$ for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains - e.g. images - by piecewise smooth functions. We introduce a fairly…
The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…
An asymptotic formula is proved for the expected $T$-functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in $\mathbb{R}^n$ according to an arbitrary positive…
We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
Flag manifolds are generalizations of projective spaces and other Grassmannians: they parametrize flags, which are nested sequences of subspaces in a given vector space. These are important objects in algebraic and differential geometry,…
We study the problem of generating a hyperplane tessellation of an arbitrary set $T$ in $\mathbb{R}^n$, ensuring that the Euclidean distance between any two points corresponds to the fraction of hyperplanes separating them up to a…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency…
We study central limit theorems for the projected sample mean of independent and identically distributed observations on subsets $\mathcal Q \subset \mathbb R^2$ of the Euclidean plane. It is well-known that two conditions suffice to obtain…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Uniform sampling of simple graphs having a given degree sequence is a known problem with exponential complexity in the square of the mean degree. For undirected graphs, randomised approximation algorithms have nonetheless been shown to…
We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar…
Given two 2-level factors of interest, a 2^2 split-plot design} (a) takes each of the $2^2=4$ possible factorial combinations as a treatment, (b) identifies one factor as `whole-plot,' (c) divides the experimental units into blocks, and (d)…