Related papers: Ridge partial correlation screening for ultrahigh-…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
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…
High-dimensional data are commonly seen in modern statistical applications, variable selection methods play indispensable roles in identifying the critical features for scientific discoveries. Traditional best subset selection methods are…
We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting…
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…
We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…
Feature screening is useful and popular to detect informative predictors for ultrahigh-dimensional data before developing proceeding statistical analysis or constructing statistical models. While a large body of feature screening procedures…
Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as…
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…
In recent years we have been able to gather large amounts of genomic data at a fast rate, creating situations where the number of variables greatly exceeds the number of observations. In these situations, most models that can handle a…
Herein, we propose a Spearman rank correlation based screening procedure for ultrahigh-dimensional data with censored response case. The proposed method is model-free without specifying any regression forms of predictors or response…
In practical applications, one often does not know the "true" structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…
Advancement in technology has generated abundant high-dimensional data that allows integration of multiple relevant studies. Due to their huge computational advantage, variable screening methods based on marginal correlation have become…
We introduce a two-step procedure, in the context of ultra-high dimensional additive models, which aims to reduce the size of covariates vector and distinguish linear and nonlinear effects among nonzero components. Our proposed screening…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
We in this paper propose a directional regression based approach for ultrahigh dimensional sufficient variable screening with censored responses. The new method is designed in a model-free manner and thus can be adapted to various complex…