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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,…
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…
Screening for ultrahigh dimensional features may encounter complicated issues such as outlying observations, heteroscedasticity or heavy-tailed distribution, multi-collinearity and confounding effects. Standard correlation-based marginal…
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…
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…
Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre screening of the variables may be necessary. A…
We consider the problem of screening features in an ultrahigh-dimensional setting. Using maximum correlation, we develop a novel procedure called MC-SIS for feature screening, and show that MC-SIS possesses the sure screen property without…
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…
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…
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…
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…
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…
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 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…
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…
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…
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…
This paper treats the problem of screening for variables with high correlations in high dimensional data in which there can be many fewer samples than variables. We focus on threshold-based correlation screening methods for three related…
Robustness has been extensively studied in reinforcement learning (RL) to handle various forms of uncertainty such as random perturbations, rare events, and malicious attacks. In this work, we consider one critical type of robustness…
High-dimensional variable selection is an important issue in many scientific fields, such as genomics. In this paper, we develop a sure independence feature screening pro- cedure based on kernel canonical correlation analysis (KCCA-SIS, for…