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We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…

Optimization and Control · Mathematics 2023-07-14 Suresh Bolusani , Ted K. Ralphs

Recent binary representation learning models usually require sophisticated binary optimization, similarity measure or even generative models as auxiliaries. However, one may wonder whether these non-trivial components are needed to…

Computer Vision and Pattern Recognition · Computer Science 2019-08-27 Yuming Shen , Jie Qin , Jiaxin Chen , Li Liu , Fan Zhu

This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…

Statistics Theory · Mathematics 2016-07-04 Nicolas Garcia Trillos , Ryan Murray

The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal…

Machine Learning · Statistics 2019-03-26 Balázs Csanád Csáji , Ambrus Tamás

Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard…

Machine Learning · Statistics 2014-11-20 Patrick K. Kimes , D. Neil Hayes , J. S. Marron , Yufeng Liu

Classification involves the learning of the mapping function that associates input samples to corresponding target label. There are two major categories of classification problems: Single-label classification and Multi-label classification.…

Machine Learning · Computer Science 2016-09-06 Meng Joo Er , Rajasekar Venkatesan , Ning Wang

While neural network binary classifiers are often evaluated on metrics such as Accuracy and $F_1$-Score, they are commonly trained with a cross-entropy objective. How can this training-evaluation gap be addressed? While specific techniques…

Machine Learning · Computer Science 2022-06-03 Nathan Tsoi , Kate Candon , Deyuan Li , Yofti Milkessa , Marynel Vázquez

In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…

Machine Learning · Computer Science 2025-12-30 Anqi Mao , Mehryar Mohri , Yutao Zhong

Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and…

Machine Learning · Computer Science 2023-10-20 Attila Fazekas , György Kovács

We study the problem of multi-class classification under system-level constraints expressible as linear functionals over randomized classifiers. We propose a post-processing approach that adjusts a given base classifier to satisfy general…

Optimization and Control · Mathematics 2025-12-17 Evgenii Chzhen , Mohamed Hebiri , Gayane Taturyan

We present a new approach for mitigating unfairness in learned classifiers. In particular, we focus on binary classification tasks over individuals from two populations, where, as our criterion for fairness, we wish to achieve similar false…

Machine Learning · Computer Science 2018-03-09 Yahav Bechavod , Katrina Ligett

We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…

Methodology · Statistics 2018-11-26 Le-Yu Chen , Sokbae Lee

Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…

Statistics Theory · Mathematics 2025-03-18 Guo Xian Yau , Chong Zhang

Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued and binary data. However, obtaining an (ideally concise) explanation via hypersphere…

Machine Learning · Computer Science 2023-12-13 Eduard Eiben , Robert Ganian , Iyad Kanj , Sebastian Ordyniak , Stefan Szeider

We introduce a simple and computationally trivial method for binary classification based on the evaluation of potential functions. We demonstrate that despite the conceptual and computational simplicity of the method its performance can…

Machine Learning · Computer Science 2008-12-17 Erik Boczko , Andrew DiLullo , Todd Young

As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional…

Machine Learning · Statistics 2020-12-25 Qing Ye , Weijun Xie

We present a systematic approach for achieving fairness in a binary classification setting. While we focus on two well-known quantitative definitions of fairness, our approach encompasses many other previously studied definitions as special…

Machine Learning · Computer Science 2018-07-17 Alekh Agarwal , Alina Beygelzimer , Miroslav Dudík , John Langford , Hanna Wallach

In this work we consider a problem of multi-label classification, where each instance is associated with some binary vector. Our focus is to find a classifier which minimizes false negative discoveries under constraints. Depending on the…

Statistics Theory · Mathematics 2019-03-29 Evgenii Chzhen

Evaluating performance across optimization algorithms on many problems presents a complex challenge due to the diversity of numerical scales involved. Traditional data processing methods, such as hypothesis testing and Bayesian inference,…

Optimization and Control · Mathematics 2024-09-10 Yunpeng Jinng , Qunfeng Liu

The increasing use of deep learning across various domains highlights the importance of understanding the decision-making processes of these black-box models. Recent research focusing on the decision boundaries of deep classifiers, relies…

Machine Learning · Computer Science 2024-08-13 Inês Gomes , Luís F. Teixeira , Jan N. van Rijn , Carlos Soares , André Restivo , Luís Cunha , Moisés Santos