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The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting.
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Multi-class support vector machines
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Statistical mechanics of support vector networks
Rainer Dietrich, Manfred Opper, and Haim Sompolinsky · 1999
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Reducing multiclass to binary: A unifying approach for margin classifiers
Erin L. Allwein, Robert E. Schapire, and Yoram Singer · 2001
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Robust learning and generalization with support vector machines
Arnaud Buhot and Mirta B Gordon · 2001
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On the algorithmic implementation of multiclass kernel-based vector machines
Koby Crammer and Yoram Singer · 2002
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Round robin classification
Johannes Fürnkranz · 2002
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Empirical Margin Distributions and Bounding the Generalization Error of Combined Classifiers
V. Koltchinskii and D. Panchenko · 2002
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Everything old is new again: a fresh look at historical approaches in machine learning
Ryan Michael Rifkin · 2002
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Rademacher and Gaussian complexities: Risk bounds and structural results
Peter L. Bartlett and Shahar Mendelson · 2003
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Multicategory support vector machines
Yoonkyung Lee, Yi Lin, and Grace Wahba · 2004
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In defense of one-vs-all classification
Ryan Rifkin and Aldebaro Klautau · 2004
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Statistical behavior and consistency of classification methods based on convex risk minimization
Tong Zhang · 2004
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Stable recovery of sparse overcomplete representations in the presence of noise
David L Donoho, Michael Elad, and Vladimir N Temlyakov · 2005
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Pac-bayesian compression bounds on the prediction error of learning algorithms for classification
Thore Graepel, Ralf Herbrich, and John Shawe-Taylor · 2005
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A statistical physics approach for the analysis of machine learning algorithms on real data
Dörthe Malzahn and Manfred Opper · 2005
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Just relax: Convex programming methods for identifying sparse signals in noise
Joel A Tropp · 2006
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On the consistency of multiclass classification methods
Ambuj Tewari and Peter L Bartlett · 2007
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Matrix mathematics: theory, facts, and formulas
Dennis S Bernstein · 2009
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Introduction to Algorithms, Third Edition
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein · 2009
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A pac-bayes sample-compression approach to kernel methods
Pascal Germain, Alexandre Lacoste, François Laviolette, Mario Marchand, and Sara Shanian · 2011
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Matrix Analysis
Roger A. Horn and Charles R. Johnson · 2012
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Cost-sensitive multiclass classification risk bounds
Bernardo Ávila Pires, Mohammad Ghavamzadeh, and Csaba Szepesvári · 2013
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Hanson-wright inequality and sub-gaussian concentration
Mark Rudelson, Roman Vershynin, et al · 2013
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The nature of statistical learning theory
Vladimir Vapnik · 2013
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Multi-class svms: From tighter data-dependent generalization bounds to novel algorithms
Yunwen Lei, Urun Dogan, Alexander Binder, and Marius Kloft · 2015
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Imagenet large scale visual recognition challenge
Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al · 2015
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Structured prediction theory based on factor graph complexity
Corinna Cortes, Vitaly Kuznetsov, Mehryar Mohri, and Scott Yang · 2016
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Squared earth mover’s distance-based loss for training deep neural networks
Le Hou, Chen-Ping Yu, and Dimitris Samaras · 2016
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A vector-contraction inequality for rademacher complexities
Andreas Maurer · 2016
Cited alongside, same era.
Tight risk bounds for multi-class margin classifiers
Yu Maximov and Daria Reshetova · 2016
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Multiclass classification calibration functions
Bernardo Ávila Pires and Csaba Szepesvári · 2016
Cited alongside, same era.
Gintare Karolina Dziugaite and Daniel M Roy · 2017
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A precise high-dimensional asymptotic theory for boosting and min-l1-norm interpolated classifiers
Tengyuan Liang and Pragya Sur · 2020
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Long-tail learning via logit adjustment
Aditya Krishna Menon, Sadeep Jayasumana, Ankit Singh Rawat, Himanshu Jain, Andreas Veit, and Sanjiv Kumar · 2020
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Neural collapse with unconstrained features
Dustin G Mixon, Hans Parshall, and Jianzong Pi · 2020
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Harmless interpolation of noisy data in regression
Vidya Muthukumar, Kailas Vodrahalli, Vignesh Subramanian, and Anant Sahai · 2020
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Prevalence of neural collapse during the terminal phase of deep learning training
Vardan Papyan, X. Y. Han, and David L. Donoho · 2020
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Generalized entropy cost function in neural networks
Krzysztof Gajowniczek, Leszek J. Chmielewski, Arkadiusz Orłowski, and Tomasz Ząbkowski · 2017
Cited alongside, same era.
Asymptotic behavior of support vector machine for spiked population model
Hanwen Huang · 2017
Cited alongside, same era.
Understanding deep learning requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2017
Cited alongside, same era.
Robust loss functions for learning multi-class classifiers
Himanshu Kumar and P. S. Sastry · 2018
Cited alongside, same era.
The implicit bias of gradient descent on separable data
Daniel Soudry, Elad Hoffer, Mor Shpigel Nacson, Suriya Gunasekar, and Nathan Srebro · 2018
Cited alongside, same era.
Reconciling modern machine-learning practice and the classical bias–variance trade-off
Mikhail Belkin, Daniel Hsu, Siyuan Ma, and Soumik Mandal · 2019
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Learning imbalanced datasets with label-distribution-aware margin loss
Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma · 2019
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Tomaso Poggio and Qianli Liao · 2020
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Explicit regularization and implicit bias in deep network classifiers trained with the square loss
Tomaso Poggio and Qianli Liao · 2020
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The performance analysis of generalized margin maximizers on separable data
Fariborz Salehi, Ehsan Abbasi, and Babak Hassibi · 2020
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Benign overfitting in ridge regression
Alexander Tsigler and Peter L Bartlett · 2020
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Theoretical insights into multiclass classification: A high-dimensional asymptotic view
Christos Thrampoulidis, Samet Oymak, and Mahdi Soltanolkotabi · 2020
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Sharp asymptotics and optimal performance for inference in binary models
Hossein Taheri, Ramtin Pedarsani, and Christos Thrampoulidis · 2020
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Multiclass classification by sparse multinomial logistic regression
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Support vector machines and linear regression coincide with very high-dimensional features
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Risk bounds for over-parameterized maximum margin classification on sub-Gaussian mixtures
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Finite-sample analysis of interpolating linear classifiers in the overparameterized regime
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A model of double descent for high-dimensional binary linear classification
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Dissecting supervised constrastive learning
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On the proliferation of support vectors in high dimensions
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Neural collapse under mse loss: Proximity to and dynamics on the central path
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On the precise error analysis of support vector machines
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Label-imbalanced and group-sensitive classification under overparameterization
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Phase transitions for one-vs-one and one-vs-all linear separability in multiclass gaussian mixtures
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Interpolating classifiers make few mistakes
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Classification vs regression in overparameterized regimes: Does the loss function matter?
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Fundamental limits of ridge-regularized empirical risk minimization in high dimensions
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A geometric analysis of neural collapse with unconstrained features
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Neural collapse under cross-entropy loss
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