Related papers: A robust variable screening procedure for ultra-hi…
Sure Independence Screening is a fast procedure for variable selection in ultra-high dimensional regression analysis. Unfortunately, its performance greatly deteriorates with increasing dependence among the predictors. To solve this issue,…
We consider the problem of variable screening in ultra-high dimensional generalized linear models (GLMs) of non-polynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a…
Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking…
This paper is concerned with screening features in ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure based on the distance…
Two popular variable screening methods under the ultra-high dimensional setting with the desirable sure screening property are the sure independence screening (SIS) and the forward regression (FR). Both are classical variable screening…
Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality $p$, estimation accuracy…
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…
As a computationally fast and working efficient tool, sure independence screening has received much attention in solving ultrahigh dimensional problems. This paper contributes two robust sure screening approaches that simultaneously take…
We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…
Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…
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…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
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…
Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model…
In ultrahigh dimensional setting, independence screening has been both theoretically and empirically proved a useful variable selection framework with low computation cost. In this work, we propose a two-step framework by using marginal…
Variable selection is a widely studied problem in high dimensional statistics, primarily since estimating the precise relationship between the covariates and the response is of great importance in many scientific disciplines. However, most…
Statistical inference can be computationally prohibitive in ultrahigh-dimensional linear models. Correlation-based variable screening, in which one leverages marginal correlations for removal of irrelevant variables from the model prior to…
Feature screening approaches are effective in selecting active features from data with ultrahigh dimensionality and increasing complexity; however, the majority of existing feature screening approaches are either restricted to a univariate…
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…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…