Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing, especially in modern regimes where the number of classes is rather large. In this paper, we take a step in this direction by providing the first asymptotically precise analysis of linear multiclass classification. Our theoretical analysis allows us to precisely characterize how the test error varies over different training algorithms, data distributions, problem dimensions as well as number of classes, inter/intra class correlations and class priors. Specifically, our analysis reveals that the classification accuracy is highly distribution-dependent with different algorithms achieving optimal performance for different data distributions and/or training/features sizes. Unlike linear regression/binary classification, the test error in multiclass classification relies on intricate functions of the trained model (e.g., correlation between some of the trained weights) whose asymptotic behavior is difficult to characterize. This challenge is already present in simple classifiers, such as those minimizing a square loss. Our novel theoretical techniques allow us to overcome some of these challenges. The insights gained may pave the way for a precise understanding of other classification algorithms beyond those studied in this paper.
Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theory
LAMSADE, Université Paris Dauphine - PSL, CNRS（巴黎-萨克雷大学LAMSADE研究所，巴黎第四大学-PSL，CNRS）；Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université（概率、统计与建模实验室，巴黎-萨克雷大学）
Consistent Multiclass Algorithms for Complex Metrics and Constraints
Google Research（谷歌研究院）；Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；Amazon Inc.（亚马逊公司）；Google Research India（谷歌印度研究院）；University of Pennsylvania（宾夕法尼亚大学）
Empirical Study of Observable Sets in Multiclass Quantum Classification
Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA)（伊克兰技术研究中心、巴斯克研究与技术联盟）；University of the Basque Country/Euskal Herriko Unibertsitatea-UPV/EHU（巴斯克大学）；Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastian, Spain（donostia国际物理中心）
Implicit Bias of Spectral Descent and Muon on Multiclass Separable Data
Department of Computer Science University of British Columbia（计算机科学系不列颠哥伦比亚大学）；University of British Columbia Canada（不列颠哥伦比亚大学加拿大）；CIFAR AI Chair (Amii) &（CIFAR人工智能主席（Amii））；Department of Electrical and Computer Engineering University of British Columbia（电气与计算机工程系不列颠哥伦比亚大学）
Navigating Healthcare Insights: A Birds Eye View of Explainability with Knowledge Graphs
Hajim School of Engineering and Applied Sciences, University of Rochester（罗切斯特大学哈吉米工程与应用科学学院）；College of Engineering and Applied Sciences, University at Albany, State University of New York（纽约州立大学奥尔巴尼分校工程与应用科学学院）；Deloitte LLC（德勤有限责任公司）
Multimodal Task-Driven Dictionary Learning for Image Classification
Pennsylvania State University（宾夕法尼亚州立大学）；Army Research Laboratory（美国陆军研究实验室）；Bosch Research and Technology Center（博世研究与技术中心）；West Virginia University（西弗吉尼亚大学）
Semantic4Safety: Causal Insights from Zero-shot Street View Imagery Segmentation for Urban Road Safety
School of Geospatial Engineering and Science, Sun Yat-sen University（地理空间工程与科学学院，中山大学）；School of Geographical and Earth Sciences, University of Glasgow（地理与地球科学学院，格拉斯哥大学）；School of Economics and Management, Shanxi University（经济学与管理学院，山西大学）
