相关论文: Interpolating Classifiers Make Few Mistakes

In this work, we investigate the behavior of ridge regression in an overparameterized binary classification task. We assume examples are drawn from (anisotropic) class-conditional cluster distributions with opposing means and we allow for…

We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural network model and the residual network model. We proved that for…

Although deep neural networks are effective on supervised learning tasks, they have been shown to be brittle. They are prone to overfitting on their training distribution and are easily fooled by small adversarial perturbations. In this…

Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes…

Few-shot learning aims to transfer the knowledge acquired from training on a diverse set of tasks to unseen tasks from the same task distribution with a limited amount of labeled data. The underlying requirement for effective few-shot…

Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator…

Standard classification treats all errors equally, but in content moderation, medical screening, and safety-critical applications, mistakes on clear-cut cases are far more costly than errors on ambiguous ones. We propose normalized excess…

We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in…

We prove that the Minimum Description Length learning rule exhibits tempered overfitting. We obtain tempered agnostic finite sample learning guarantees and characterize the asymptotic behavior in the presence of random label noise.

We study the close interplay between error and compression in the non-parametric multiclass classification setting in terms of prototype learning rules. We focus in particular on a recently proposed compression-based learning rule termed…

We propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly…

It has been recently observed in much of the literature that neural networks exhibit a bottleneck rank property: for larger depths, the activation and weights of neural networks trained with gradient-based methods tend to be of…

We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first…

In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in…

We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius…

In real word applications, data generating process for training a machine learning model often differs from what the model encounters in the test stage. Understanding how and whether machine learning models generalize under such…

We bound the excess risk of interpolating deep linear networks trained using gradient flow. In a setting previously used to establish risk bounds for the minimum $\ell_2$-norm interpolant, we show that randomly initialized deep linear…

Interpolation models are critical for a wide range of applications, from numerical optimization to artificial intelligence. The reliability of the provided interpolated value is of utmost importance, and it is crucial to avoid the…

We investigate the learning dynamics of classifiers in scenarios where classes are separable or classifiers are over-parameterized. In both cases, Empirical Risk Minimization (ERM) results in zero training error. However, there are many…