Related papers: Lecture notes on ridge regression
Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood…
We propose a ridge-penalized adaptive Mantel test (AdaMant) for evaluating the association of two high-dimensional sets of features. By introducing a ridge penalty, AdaMant tests the association across many metrics simultaneously. We…
Linear regression is often deemed inherently interpretable; however, challenges arise for high-dimensional data. We focus on further understanding how linear regression approximates nonlinear responses from high-dimensional functional data,…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the…
Penalized selection criteria like AIC or BIC are among the most popular methods for variable selection. Their theoretical properties have been studied intensively and are well understood, but making use of them in case of high-dimensional…
This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed…
We consider standard gradient descent, gradient flow and conjugate gradients as iterative algorithms for minimising a penalised ridge criterion in linear regression. While it is well known that conjugate gradients exhibit fast numerical…
This article explores the estimation of precision matrices in high-dimensional Gaussian graphical models. We address the challenge of improving the accuracy of maximum likelihood-based precision estimation through penalization.…
Decisions are increasingly taken by both humans and machine learning models. However, machine learning models are currently trained for full automation -- they are not aware that some of the decisions may still be taken by humans. In this…
Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of…
This paper is concerned with the selection of fixed effects along with the estimation of fixed effects, random effects and variance components in the linear mixed-effects model. We introduce a selection procedure based on an adaptive ridge…
We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
In many areas, practitioners need to analyze large datasets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental…
Data collected from a bike-sharing system exhibit complex temporal and spatial features. We analyze shared-bike usage data collected in three large cities at the level of individual stations, accounting for station-specific behavior and…
We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one…
In projection pursuit regression (PPR), an unknown response function is approximated by the sum of M "ridge functions," which are flexible functions of one-dimensional projections of a multivariate input space. Traditionally, optimization…