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The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…

Algorithmic fairness is receiving significant attention in the academic and broader literature due to the increasing use of predictive algorithms, including those based on artificial intelligence. One benefit of this trend is that algorithm…

Many organizations use algorithms that have a disparate impact, i.e., the benefits or harms of the algorithm fall disproportionately on certain social groups. Addressing an algorithm's disparate impact can be challenging, however, because…

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

The digitalization of credit scoring has become essential for financial institutions and commercial banks, especially in the era of digital transformation. Machine learning techniques are commonly used to evaluate customers'…

In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…

With growing applications of Machine Learning (ML) techniques in the real world, it is highly important to ensure that these models work in an equitable manner. One main step in ensuring fairness is to effectively measure fairness, and to…

Assessing uncertainty is an important step towards ensuring the safety and reliability of machine learning systems. Existing uncertainty estimation techniques may fail when their modeling assumptions are not met, e.g. when the data…

Algorithmic fairness has gained prominence due to societal and regulatory concerns about biases in Machine Learning models. Common group fairness metrics like Equalized Odds for classification or Demographic Parity for both classification…

Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…

The experimental evaluation of algorithms results in a large set of data which generally do not follow a normal distribution or are not heteroscedastic. Besides, some of its entries may be missing, due to the inability of an algorithm to…

Machine-learned systems are in widespread use for making decisions about humans, and it is important that they are fair, i.e., not biased against individuals based on sensitive attributes. We present runtime verification of algorithmic…

Missing data are prevalent and present daunting challenges in real data analysis. While there is a growing body of literature on fairness in analysis of fully observed data, there has been little theoretical work on investigating fairness…

Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the…

In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…

We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…

Fairness is an important performance criterion in all resource allocation schemes, including those in distributed computer systems. However, it is often specified only qualitatively. The quantitative measures proposed in the literature are…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…

Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…