Related papers: On the Supremum of Some Random Dirichlet Polynomia…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
We consider arbitrary open sets $\Omega$ in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of $\Omega$, (ii) the number of Courant-sharp Dirichlet eigenvalues of…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…
We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the…
We give an upper bound in O(d ^((n+1)/2)) for the number of critical points of a normal random polynomial with degree d and at most n variables. Using the large deviation principle for the spectral value of large random matrices we obtain…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
This article presents some interesting and novel results concerning the average modulus of random polynomials on the unit circle and the unit disc, with coefficients distributed as standard normal variates. The paper also introduces new…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…