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

We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…

Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement…

A new generalized ridge regression shrinkage path is proposed that is as short as possible under the restriction that it must pass through the vector of regression coefficient estimators that make the overall Optimal Variance-Bias Trade-Off…

We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…

Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^{\gamma}$ for some $\gamma > 0$.…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Numerous recent works show that overparameterization implicitly reduces variance for min-norm interpolators and max-margin classifiers. These findings suggest that ridge regularization has vanishing benefits in high dimensions. We challenge…

We present the first optimal rates for infinite-dimensional vector-valued ridge regression on a continuous scale of norms that interpolate between $L_2$ and the hypothesis space, which we consider as a vector-valued reproducing kernel…

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient…

This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis…

We consider the linear model $\mathbf{y} = \mathbf{X} \mathbf{\beta}_\star + \mathbf{\epsilon}$ with $\mathbf{X}\in \mathbb{R}^{n\times p}$ in the overparameterized regime $p>n$. We estimate $\mathbf{\beta}_\star$ via generalized (weighted)…

Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…

Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…

Regularization is an essential element of virtually all kernel methods for nonparametric regression problems. A critical factor in the effectiveness of a given kernel method is the type of regularization that is employed. This article…

Backdoor and data-poisoning attacks can flip predictions with tiny training corruptions, yet a sharp theory linking poisoning strength, overparameterization, and regularization is lacking. We analyze ridge least squares with an unpenalized…

This work studies finite-sample properties of the risk of the minimum-norm interpolating predictor in high-dimensional regression models. If the effective rank of the covariance matrix $\Sigma$ of the $p$ regression features is much larger…

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…

We study the flexible piecewise exponential model in a high dimensional setting where the number of covariates $p$ grows proportionally to the number of observations $n$ and under the hypothesis of random uncorrelated Gaussian designs. We…

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider…