Related papers: On the consistency theory of high dimensional vari…
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…
We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature…
Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the…
Modern biotechnologies often result in high-dimensional data sets with much more variables than observations (n $\ll$ p). These data sets pose new challenges to statistical analysis: Variable selection becomes one of the most important…
Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or…
We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in…
Feature screening for ultrahigh-dimension, in general, proceeds with two essential steps. The first step is measuring and ranking the marginal dependence between response and covariates, and the second is determining the threshold. We…
Variable selection in high dimensional space has challenged many contemporary statistical problems from many frontiers of scientific disciplines. Recent technology advance has made it possible to collect a huge amount of covariate…
In data sets with many more features than observations, independent screening based on all univariate regression models leads to a computationally convenient variable selection method. Recent efforts have shown that in the case of…
Support Vector Data Description (SVDD) is a popular one-class classifiers for anomaly and novelty detection. But despite its effectiveness, SVDD does not scale well with data size. To avoid prohibitive training times, sampling methods…
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…
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…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
Screening methods are useful tools for variable selection in regression analysis when the number of predictors is much larger than the sample size. Factor analysis is used to eliminate multicollinearity among predictors, which improves the…
Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we…
The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core problem is the estimation of the number of samples needed in order to secure a stable and…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
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…
We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form…
For many practical problems, the regression models follow the strong heredity property (also known as the marginality), which means they include parent main effects when a second-order effect is present. Existing methods rely mostly on…