相关论文: Azuma-Hoeffding bounds for a class of urn models
We establish an Azuma type inequality under a Lipshitz condition for martingales in the framework of noncommutative probability spaces and apply it to deduce a noncommutative Heoffding inequality as well as a noncommutative McDiarmid type…
This paper first introduces a refined version of the Azuma-Hoeffding inequality for discrete-parameter martingales with uniformly bounded jumps. The refined inequality is used to revisit the large deviations analysis of binary hypothesis…
Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…
This paper is focused on the moderate-deviations analysis of binary hypothesis testing. The analysis relies on a concentration inequality for discrete-parameter martingales with bounded jumps, where this inequality forms a refinement to the…
Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…
Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between of two real $n$-vectors. We derive probabilistic perturbation bounds, as well as probabilistic…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
We consider a two-particle quantum systems in a d-dimensional Euclidean space with interaction and in presence of a random external potential (a continuous two-particle Anderson model). We establish Wegner-type estimates (inequalities) for…
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…
The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…
We propose a method for obtaining rigorous and accurate upper and lower bounds on the eigenvalues of ordinary and partial differential operators in bounded regions of Euclidean space. It uses a boundary condition homotopy method starting…
The quality of numerical computations can be measured through their forward error, for which finding good error bounds is challenging in general. For several algorithms and using stochastic rounding (SR), probabilistic analysis has been…
In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where…
Consider the multicolored urn model where, after every draw, balls of the different colors are added to the urn in a proportion determined by a given stochastic replacement matrix. We consider some special replacement matrices which are not…
We derive two probabilistic bounds for the relative forward error in the floating point summation of $n$ real numbers, by representing the roundoffs as independent, zero-mean, bounded random variables. The first probabilistic bound is based…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
This paper develops a new dimension-free Azuma-Hoeffding type bound on summation norm of a martingale difference sequence with random individual bounds. With this novel result, we provide high-probability bounds for the gradient norm…
We consider the problem of deriving upper bounds on the parameters of sum-rank-metric codes, with focus on their dimension and block length. The sum-rank metric is a combination of the Hamming and the rank metric, and most of the available…