Related papers: Spectral-Transport Stability and Benign Overfittin…

We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…

Interoception and exteroception provide continuous feedback about the body and the environment, yet how they are dynamically integrated within a unified predictive coding framework has remained under-specified. This paper develops and…

Deep-learning models for traffic data prediction can have superior performance in modeling complex functions using a multi-layer architecture. However, a major drawback of these approaches is that most of these approaches do not offer…

In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…

In this paper, we tackle the transductive semi-supervised learning problem that aims to obtain label predictions for the given unlabeled data points according to Vapnik's principle. Our proposed approach is based on optimal transport, a…

Recent empirical and theoretical studies have established the generalization capabilities of large machine learning models that are trained to (approximately or exactly) fit noisy data. In this work, we prove a surprising result that even…

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

We consider regularised quadratic optimal transport with subquadratic polynomial or entropic regularisation. In both cases, we prove interior Lipschitz-estimates on a transport-like map and interior gradient Lipschitz-estimates on the…

Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. Since such bounds often hold uniformly over all parameters, they suffer from over-parametrization and fail to account…

Although numerous methods to reduce the overfitting of convolutional neural networks (CNNs) exist, it is still not clear how to confidently measure the degree of overfitting. A metric reflecting the overfitting level might be, however,…

This paper addresses the string stabilization of vehicular platooning when stochastic phenomena are inherent in inter-vehicle communication. To achieve this, we first provide two definitions to analytically assess the string stability in…

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…

This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…

Many common estimators in machine learning and causal inference are linear smoothers, where the prediction is a weighted average of the training outcomes. Some estimators, such as ordinary least squares and kernel ridge regression, allow…

A widely used algorithm for transfer learning is fine-tuning, where a pre-trained model is fine-tuned on a target task with a small amount of labeled data. When the capacity of the pre-trained model is significantly larger than the size of…

Models with nonlinear architectures/parameterizations such as deep neural networks (DNNs) are well known for their mysteriously good generalization performance at overparameterization. In this work, we tackle this mystery from a novel…

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…

Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By…

Modern neural networks are typically trained in an over-parameterized regime where the parameters of the model far exceed the size of the training data. Such neural networks in principle have the capacity to (over)fit any set of labels…

Unmeasured confounders are a major source of bias in regression-based effect estimation and causal inference. In this paper, we advocate a new profiled transfer learning framework, ProTrans, to address confounding effects in the target…