Related papers: The BRS-inequality and its Applications A Survey
We propose a new family of fairness definitions for classification problems that combine some of the best properties of both statistical and individual notions of fairness. We posit not only a distribution over individuals, but also a…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
Many statistical methods require solutions to optimization problems. When the global solution is hard to attain, statisticians always use the better if there are two solutions for chosen, where the word "better" is understood in the sense…
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…
A large class of stochastic programs involve optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the…
The first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for the "hard" part of Tsirelson's theorem. In the final part we…
We compute a variance lower bound for unbiased estimators in specified statistical models. The construction of the bound is related to the original Cram\'er-Rao bound, although it does not require the differentiability of the model.…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
For most of the history of information retrieval (IR), search results were designed for human consumers who could scan, filter, and discard irrelevant information on their own. This shaped retrieval systems to optimize for finding and…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
In this paper, we introduce the increasing belief criterion in association rule mining. The criterion uses a recursive application of Bayes' theorem to compute a rule's belief. Extracted rules are required to have their belief increase with…
In theory, the probabilistic linkage method provides two distinct advantages over non-probabilistic methods, including minimal rates of linkage error and accurate measures of these rates for data users. However, implementations can fall…
Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…
We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
The majority of recent works investigating the link between non-locality and randomness, e.g. in the context of device-independent cryptography, do so with respect to some specific Bell inequality, usually the CHSH inequality. However, the…
We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…