Related papers: Ridge partial correlation screening for ultrahigh-…

We propose a data-driven sensor-selection algorithm for accurate estimation of the target variables from the selected measurements. The target variables are assumed to be estimated by a ridge-regression estimator which is trained based on…

Tracking and measuring targets using a variety of sensors mounted on UAVs is an effective means to quickly and accurately locate the target. This paper proposes a fusion localization method based on ridge estimation, combining the…

We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small…

Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…

This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where…

Although much progress has been made in classification with high-dimensional features \citep{Fan_Fan:2008, JGuo:2010, CaiSun:2014, PRXu:2014}, classification with ultrahigh-dimensional features, wherein the features much outnumber the…

A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To…

High-dimensional biomarkers such as genomics are increasingly being measured in randomized clinical trials. Consequently, there is a growing interest in developing methods that improve the power to detect biomarker-treatment interactions.…

This paper proposes a new feature screening method for the multi-response ultrahigh dimensional linear model by empirical likelihood. Through a multivariate moment condition, the empirical likelihood induced ranking statistics can exploit…

Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to…

Semi-competing risks data arise when both non-terminal and terminal events are considered in a model. Such data with multiple events of interest are frequently encountered in medical research and clinical trials. In this framework, terminal…

We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…

We study the following three fundamental problems about ridge regression: (1) what is the structure of the estimator? (2) how to correctly use cross-validation to choose the regularization parameter? and (3) how to accelerate computation…

We derive the ideal train/test split for the ridge regression to high accuracy in the limit that the number of training rows m becomes large. The split must depend on the ridge tuning parameter, alpha, but we find that the dependence is…

The performance of penalized likelihood approaches depends profoundly on the selection of the tuning parameter; however, there is no commonly agreed-upon criterion for choosing the tuning parameter. Moreover, penalized likelihood estimation…

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…

Gini distance correlation (GDC) was recently proposed to measure the dependence between a categorical variable, Y, and a numerical random vector, X. It mutually characterizes independence between X and Y. In this article, we utilize the GDC…

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary…

Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…

We consider $L^2$-regularized linear (ridge) regression over a finite data sample $X$ with bounded covariance and linear prediction targets $y$ with additive isotropic noise of finite variance. We present an iterative procedure to compute…