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Vignesh Subramanian

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NeurIPS Conference 2022 Conference Paper

Generalization for multiclass classification with overparameterized linear models

Vignesh Subramanian
Rahul Arya
Anant Sahai

Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying features and the number of classes scale with the number of training points. The survival/contamination analysis framework for understanding the behavior of overparameterized learning problems is adapted to this setting, revealing that multiclass classification qualitatively behaves like binary classification in that, as long as there are not too many classes (made precise in the paper), it is possible to generalize well even in settings where regression tasks would not generalize. Besides various technical challenges, it turns out that the key difference from the binary classification setting is that there are relatively fewer training examples of each class in the multiclass setting as the number of classes increases, making the multiclass problem ``harder'' than the binary one.

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JMLR Journal 2021 Journal Article

Classification vs regression in overparameterized regimes: Does the loss function matter?

Vidya Muthukumar
Adhyyan Narang
Vignesh Subramanian
Mikhail Belkin
Daniel Hsu
Anant Sahai

We compare classification and regression tasks in an overparameterized linear model with Gaussian features. On the one hand, we show that with sufficient overparameterization all training points are support vectors: solutions obtained by least-squares minimum-norm interpolation, typically used for regression, are identical to those produced by the hard-margin support vector machine (SVM) that minimizes the hinge loss, typically used for training classifiers. On the other hand, we show that there exist regimes where these interpolating solutions generalize well when evaluated by the 0-1 test loss function, but do not generalize if evaluated by the square loss function, i.e. they approach the null risk. Our results demonstrate the very different roles and properties of loss functions used at the training phase (optimization) and the testing phase (generalization). [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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