Related papers: Normal approximation for statistics of randomly we…
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic…
We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the…
We prove that a suitably de-biased version of Chatterjee's rank correlation based on i.i.d. copies of a random vector $(X,Y)$ is asymptotically normal whenever $Y$ is not almost surely constant. No further conditions on the joint…
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…
We give a simple approximation algorithm for a common generalization of many previously studied extensions of the maximum size stable matching problem with ties. These generalizations include the existence of critical vertices in the graph,…
The well-known 1-2-3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with $1$, $2$ and $3$ so that adjacent vertices receive distinct weighted degrees. This is open in general, while it is known to be…
We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…
We investigate the behavior of vertex-weighted exponential random graphs. We show that vertex-weighted exponential random graphs with edge weights induced by products of independent vertex weights are approximate mixtures of graphs whose…
We present a concentration result concerning random weighted projections in high dimensional spaces. As applications, we prove (1) New concentration inequalities for random quadratic forms; (2) The infinity norm of most unit eigenvectors of…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling…
The general aim of manifold estimation is reconstructing, by statistical methods, an $m$-dimensional compact manifold $S$ on ${\mathbb R}^d$ (with $m\leq d$) or estimating some relevant quantities related to the geometric properties of $S$.…
Small regularizers can preserve linear programming solutions exactly. This paper provides the first average-case analysis of exact regularization: with a standard Gaussian cost vector and fixed constraint set, bounds are established for the…
We study rational approximation properties for successive powers of extremal numbers defined by Roy. For $n\in{\{1,2\}}$, the classic approximation constants $\lambda_{n}(\zeta),\hat{\lambda}_{n}(\zeta),w_{n}(\zeta),\hat{w}_{n}(\zeta)$…
This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functionals, thereby improving on the previously used assumption of…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
We consider solutions to an elliptic partial differential equation in $\mathbb{R}^d$ with a stationary, random conductivity coefficient. The boundary condition on a square domain of width $L$ is chosen so that the solution has a macroscopic…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…