Related papers: Dependency-dependent Bounds for Sums of Dependent …
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints.…
We study the large deviations of sums of correlated random variables described by a matrix product ansatz, which generalizes the product structure of independent random variables to matrices whose non-commutativity is the source of…
A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…
Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this…
We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in literature with novel objects appearing in the limits. In…
In this paper we characterize the limiting behavior of sums of extreme values of long range dependent sequences defined as functionals of linear processes with finite variance. The extremal sums behave completely different by compared to…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…
In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method together with a concentration inequality approach. We…
We leverage proof techniques Fourier analysis and an existing result in coding theory to derive new bounds for the problem of non-interactive simulation of binary random variables. Previous bounds in the literature were derived by applying…
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…
When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…