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In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the…

Machine Learning · Computer Science 2025-12-02 Francesco Marchetti , Edoardo Legnaro , Sabrina Guastavino

This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially…

Machine Learning · Computer Science 2015-06-16 Yunwen Lei , Ürün Dogan , Alexander Binder , Marius Kloft

Classification is a fundamental task in machine learning. While conventional methods-such as binary, multiclass, and multi-label classification-are effective for simpler problems, they may not adequately address the complexities of some…

Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…

Machine Learning · Computer Science 2023-02-13 Jack Valmadre

In the supervised binary classification setting, score-oriented losses have been introduced with the aim of optimizing a chosen performance metric directly during the training phase, thus avoiding \textit{a posteriori} threshold tuning. To…

Machine Learning · Computer Science 2025-12-01 Francesco Marchetti , Edoardo Legnaro , Sabrina Guastavino

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective…

Machine Learning · Computer Science 2019-10-29 Meelis Kull , Miquel Perello-Nieto , Markus Kängsepp , Telmo Silva Filho , Hao Song , Peter Flach

In this paper we discuss a novel framework for multiclass learning, defined by a suitable coding/decoding strategy, namely the simplex coding, that allows to generalize to multiple classes a relaxation approach commonly used in binary…

Machine Learning · Statistics 2015-03-20 Youssef Mroueh , Tomaso Poggio , Lorenzo Rosasco , Jean-Jacques Slotine

Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of…

Background With microarray technology becoming mature and popular, the selection and use of a small number of relevant genes for accurate classification of samples is a hot topic in the circles of biostatistics and bioinformatics. However,…

Methodology · Statistics 2014-03-05 Suyan Tian , Mayte Suárez-Fariñas

Model evaluation is of crucial importance in modern statistics application. The construction of ROC and calculation of AUC have been widely used for binary classification evaluation. Recent research generalizing the ROC/AUC analysis to…

Machine Learning · Statistics 2024-04-23 Liang Wang , Luis Carvalho

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

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,…

Machine Learning · Computer Science 2020-11-17 Christos Thrampoulidis , Samet Oymak , Mahdi Soltanolkotabi

This paper introduces a framework for post-processing machine learning models so that their predictions satisfy multi-group fairness guarantees. Based on the celebrated notion of multicalibration, we introduce $(\mathbf{s},\mathcal{G},…

Machine Learning · Statistics 2024-05-06 Lujing Zhang , Aaron Roth , Linjun Zhang

Classification performance is often not uniform over the data. Some areas in the input space are easier to classify than others. Features that hold information about the "difficulty" of the data may be non-discriminative and are therefore…

Machine Learning · Computer Science 2016-05-24 Oran Richman , Shie Mannor

Multi-class text classification is one of the key problems in machine learning and natural language processing. Emerging neural networks deal with the problem using a multi-output softmax layer and achieve substantial progress, but they do…

Computation and Language · Computer Science 2020-03-26 Haiyang Xu , Junwen Chen , Kun Han , Xiangang Li

Ensuring that classifiers are well-calibrated, i.e., their predictions align with observed frequencies, is a minimal and fundamental requirement for classifiers to be viewed as trustworthy. Existing methods for assessing multiclass…

Machine Learning · Computer Science 2025-10-30 Mahmoud Hegazy , Michael I. Jordan , Aymeric Dieuleveut

We learn about the world from a diverse range of sensory information. Automated systems lack this ability as investigation has centred on processing information presented in a single form. Adapting architectures to learn from multiple…

Machine Learning · Computer Science 2020-10-27 Jason Armitage , Shramana Thakur , Rishi Tripathi , Jens Lehmann , Maria Maleshkova

We theoretically analyze and compare the following five popular multiclass classification methods: One vs. All, All Pairs, Tree-based classifiers, Error Correcting Output Codes (ECOC) with randomly generated code matrices, and Multiclass…

Machine Learning · Computer Science 2013-02-19 Amit Daniely , Sivan Sabato , Shai Shalev Shwartz

Multi-label classification (MLC) requires predicting multiple labels per sample, often under heavy class imbalance and noisy conditions. Traditional approaches apply fixed thresholds or treat labels independently, overlooking context and…

Machine Learning · Computer Science 2025-05-07 Dmytro Shamatrin

In this paper we consider high-dimensional multiclass classification by sparse multinomial logistic regression. We propose first a feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size…

Statistics Theory · Mathematics 2020-11-20 Felix Abramovich , Vadim Grinshtein , Tomer Levy
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