Related papers: Harmful Overfitting in Sobolev Spaces
This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning where data from diverse distributions are available. Min-norm interpolators emerge naturally as implicit regularized limits of…
The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal…
We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…
We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the…
Label noise in training data can significantly degrade a model's generalization performance for supervised learning tasks. Here we focus on the problem that noisy labels are primarily mislabeled samples, which tend to be concentrated near…
We study the use of linear regression for multiclass classification in the over-parametrized regime where some of the training data is mislabeled. In such scenarios it is necessary to add an explicit regularization term, $\lambda f(w)$, for…
We prove bounds on the population risk of the maximum margin algorithm for two-class linear classification. For linearly separable training data, the maximum margin algorithm has been shown in previous work to be equivalent to a limit of…
This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the…
We consider bounds on the generalization performance of the least-norm linear regressor, in the over-parameterized regime where it can interpolate the data. We describe a sense in which any generalization bound of a type that is commonly…
Modern deep neural networks are highly over-parameterized compared to the data on which they are trained, yet they often generalize remarkably well. A flurry of recent work has asked: why do deep networks not overfit to their training data?…
This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov…
Labelling of data for supervised learning can be costly and time-consuming and the risk of incorporating label noise in large data sets is imminent. When training a flexible discriminative model using a strictly proper loss, such noise will…
We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE), with linear regression models. As the development of machine learning for causal inference, a wide range of large-scale models for…
A common way to avoid overfitting in supervised learning is early stopping, where a held-out set is used for iterative evaluation during training to find a sweet spot in the number of training steps that gives maximum generalization.…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…
Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this…
We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…
State-of-the-art deep learning classifiers are heavily overparameterized with respect to the amount of training examples and observed to generalize well on "clean" data, but be highly susceptible to infinitesmal adversarial perturbations.…
Adversarial training is a widely used method to improve the robustness of deep neural networks (DNNs) over adversarial perturbations. However, it is empirically observed that adversarial training on over-parameterized networks often suffers…
In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general class of objective functions. Our class of objective functions…