Related papers: Optimal upper bounds on expected kth record values…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

We consider the regular model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad et. al. We derive an upper bound on the satisfiability threshold and NAE-satisfiability threshold for regular random $k$-SAT for any…

We establish two-sided bounds for expectations of order statistics ($k$-th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants…

We provide an efficient algorithm to generate random samples from the bounded kth order statistic in a sample of independent, but not necessarily identically distributed, random variables. The bounds can be upper or lower bounds and need…

We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…

Let $K(=K_{n,\theta})$ be a positive integer-valued random variable whose distribution is given by ${\rm P}(K = x) = \bar{s}(n,x) \theta^x/(\theta)_n$ $(x=1,\ldots,n) $, where $\theta$ is a positive number, $n$ is a positive integer,…

We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution rho. The running record equals the maximum of all elements in the sequence up…

The following anticoncentration property is proved. The probability that the $k$-order statistic of an arbitrarily correlated jointly Gaussian random vector $X$ with unit variance components lies within an interval of length $\varepsilon$…

We build optimal exponential bounds for the probabilities of large deviations of sums \sum_{k=1}^nf(X_k) where (X_k) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean…

Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or…

A standard approach to confidence intervals for quantiles requires good estimates of the quantile density. The optimal bandwidth for kernel estimation of the quantile density depends on an underlying location-scale family only through the…

This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…

Conformal Prediction is a widely studied technique to construct prediction sets of future observations. Most conformal prediction methods focus on achieving the necessary coverage guarantees, but do not provide formal guarantees on the size…

Let m and r be two integers. Let G be a connected r-regular graph of order n and k an integer depending on m and r. For even kn, we find a best upper bound (in terms of r and m) on the third largest eigenvalue that is sufficient to…

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of…

This paper generalizes and unifies the existing spectral bounds on the $k$-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than $k$. The previous bounds known in the literature…

In the context of this paper, a record is an entry in a sequence of random variables (RV's) that is larger or smaller than all previous entries. After a brief review of the classic theory of records, which is largely restricted to sequences…

Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…

The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…

In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a…