相关论文: Optimal ridge penalty for real-world high-dimensio…

The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…

In high dimensional regression, where the number of covariates is of the order of the number of observations, ridge penalization is often used as a remedy against overfitting. Unfortunately, for correlated covariates such regularisation…

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily)…

We introduce an original method of multidimensional ridge penalization in functional local linear regressions. The nonparametric regression of functional data is extended from its multivariate counterpart, and is known to be sensitive to…

Many statistical problems can be reduced to a linear inverse problem in which only a noisy version of the operator is available. Particular examples include random design regression, deconvolution problem, instrumental variable regression,…

Recently, deep neural networks have been found to nearly interpolate training data but still generalize well in various applications. To help understand such a phenomenon, it has been of interest to analyze the ridge estimator and its…

We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do…

In many modern applications of deep learning the neural network has many more parameters than the data points used for its training. Motivated by those practices, a large body of recent theoretical research has been devoted to studying…

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine…

High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…

Hastie et al. (2022) found that ridge regularization is essential in high dimensional linear regression $y=\beta^Tx + \epsilon$ with isotropic co-variates $x\in \mathbb{R}^d$ and $n$ samples at fixed $d/n$. However, Hastie et al. (2022)…

Subsampling is a popular approach to alleviating the computational burden for analyzing massive datasets. Recent efforts have been devoted to various statistical models without explicit regularization. In this paper, we develop an efficient…

Logistic regression is a ubiquitous method for probabilistic classification. However, the effectiveness of logistic regression depends upon careful and relatively computationally expensive tuning, especially for the regularisation…

Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows…

Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are…

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally…

In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning. One should…

Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to…

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…