Related papers: Introduction to Concentration Inequalities
Clustering is a fundamental problem in machine learning and operations research. Therefore, given the fact that fairness considerations have become of paramount importance in algorithm design, fairness in clustering has received significant…
Concentration inequalities are widely used for analyzing machine learning algorithms. However, current concentration inequalities cannot be applied to some of the most popular deep neural networks, notably in natural language processing.…
Recent years have seen the rapid development of fairness-aware machine learning in mitigating unfairness or discrimination in decision-making in a wide range of applications. However, much less attention has been paid to the fairness-aware…
The rapid developments of various machine learning models and their deployments in several applications has led to discussions around the importance of looking beyond the accuracies of these models. Fairness of such models is one such…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
During the last two decades, concentration inequalities have been the subject of exciting developments in various areas, including convex geometry, functional analysis, statistical physics, high-dimensional statistics, pure and applied…
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training…
Machine learning has significantly enhanced the abilities of robots, enabling them to perform a wide range of tasks in human environments and adapt to our uncertain real world. Recent works in various machine learning domains have…
Fair machine learning is receiving an increasing attention in machine learning fields. Researchers in fair learning have developed correlation or association-based measures such as demographic disparity, mistreatment disparity, calibration,…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
The more AI-assisted decisions affect people's lives, the more important the fairness of such decisions becomes. In this chapter, we provide an introduction to research on fairness in machine learning. We explain the main fairness…
Machine learning models are becoming pervasive in high-stakes applications. Despite their clear benefits in terms of performance, the models could show discrimination against minority groups and result in fairness issues in a…
This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…
Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…
Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
This paper applies several concentration inequalities to prove concentration results for the crest factor of OFDM signals. The considered approaches are, to the best of our knowledge, new in the context of establishing concentration for…
We introduce behavioral inequalities as a way to model dynamical systems defined by inequalities among their variables of interest. We claim that such a formulation enables the representation of safety-aware dynamical systems, systems with…
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
Algorithmic fairness is a major concern in recent years as the influence of machine learning algorithms becomes more widespread. In this paper, we investigate the issue of algorithmic fairness from a network-centric perspective.…