相关论文: Some notes on a method for proving inequalities by…
In order to nd a non-negative solution to a system of inequalities, the corresponding dual problem is composed, which has a suitable unity basic matrix. In such a formulation, the objective function is replaced by set of constraints based…
Algorithmic fairness is frequently motivated in terms of a trade-off in which overall performance is decreased so as to improve performance on disadvantaged groups where the algorithm would otherwise be less accurate. Contrary to this, we…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
Algorithmic decision making systems are ubiquitous across a wide variety of online as well as offline services. These systems rely on complex learning methods and vast amounts of data to optimize the service functionality, satisfaction of…
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…
We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under…
The ellipsoid algorithm is a fundamental algorithm for computing a solution to the system of $m$ linear inequalities in $n$ variables $(P): A^{\top}x \le u$ when its set of solutions has positive volume. However, when $(P)$ is infeasible,…
In this paper, we present an empirical study on image recognition fairness, i.e., extreme class accuracy disparity on balanced data like ImageNet. We experimentally demonstrate that classes are not equal and the fairness issue is prevalent…
Frequently, a set of objects has to be evaluated by a panel of assessors, but not every object is assessed by every assessor. A problem facing such panels is how to take into account different standards amongst panel members and varying…
We study the computational complexity of a robust version of the problem of testing two univariate C-finite functions for eventual inequality at large times. Specifically, working in the bit-model of real computation, we consider the…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
Decision makers increasingly rely on algorithmic risk scores to determine access to binary treatments including bail, loans, and medical interventions. In these settings, we reconcile two fairness criteria that were previously shown to be…
In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and…
We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.
Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…
The classical Remez inequality bounds the maximum of the absolute value of a polynomial $P(x)$ of degree $d$ on $[-1,1]$ through the maximum of its absolute value on any subset $Z$ of positive measure in $[-1,1]$. It was shown in…
A procedure is suggested for testing the resolution and comparing the relative accuracy of numerical schemes for integration of the incompressible Euler equations.
Early studies of risk assessment algorithms used in criminal justice revealed widespread racial biases. In response, machine learning researchers have developed methods for fairness, many of which rely on equalizing empirical metrics across…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…