Related papers: Some notes on a method for proving inequalities by…

In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.

We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with…

As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…

Efforts to promote equitable public policy with algorithms appear to be fundamentally constrained by the "impossibility of fairness" (an incompatibility between mathematical definitions of fairness). This technical limitation raises a…

We explore the following question: Is a decision-making program fair, for some useful definition of fairness? First, we describe how several algorithmic fairness questions can be phrased as program verification problems. Second, we discuss…

Discrimination via algorithmic decision making has received considerable attention. Prior work largely focuses on defining conditions for fairness, but does not define satisfactory measures of algorithmic unfairness. In this paper, we focus…

In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Machine learning models are increasingly deployed for critical decision-making tasks, making it important to verify that they do not contain gender or racial biases picked up from training data. Typical approaches to achieve fairness…

As machine learning systems are increasingly used to make real world legal and financial decisions, it is of paramount importance that we develop algorithms to verify that these systems do not discriminate against minorities. We design a…

With the increased use of machine learning systems for decision making, questions about the fairness properties of such systems start to take center stage. Most existing work on algorithmic fairness assume complete observation of features…

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as…

Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total'' error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on…

This paper proposes a method for measuring fairness through equality of effort by applying algorithmic recourse through minimal interventions. Equality of effort is a property that can be quantified at both the individual and the group…

By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…

The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to…

Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear…