Entropy-based model-free feature screening for ultrahigh-dimensional multiclass classification

Most feature screening methods for ultrahigh-dimensional classification explicitly or implicitly assume the covariates are continuous. However, in the practice, it is quite common that both categorical and continuous covariates appear in the data, and applicable feature screening method is very limited. To handle this non-trivial situation, we propose an entropy-based feature screening method, which is model free and provides a unified screening procedure for both categorical and continuous covariates. We establish the sure screening and ranking consistency properties of the proposed procedure. We investigate the finite sample performance of the proposed procedure by simulation studies and illustrate the method by a real data analysis.     

Quantile screening for ultra-high-dimensional heterogeneous data conditional on some variables

In this paper, we propose a conditional quantile independence screening approach for ultra-high-dimensional heterogeneous data given some known, significant and low-dimensional variables. The new method does not require imposing a specific model structure for the response and covariates and can detect additional features that contribute to conditional quantiles of the response given those already-identified important predictors. We also prove that the proposed procedure enjoys the ranking consistency and sure screening properties. Some simulation studies are carried out to examine the performance of advised procedure. At last, we illustrate it by a real data example.     

Variable screening for ultrahigh dimensional censored quantile regression

Quantile regression is a flexible approach to assessing covariate effects on failure time, which has attracted considerable interest in survival analysis. When the dimension of covariates is much larger than the sample size, feature screening and variable selection become extremely important and indispensable. In this article, we introduce a new feature screening method for ultrahigh dimensional censored quantile regression. The proposed method can work for a general class of survival models, allow for heterogeneity of data and enjoy desirable properties including the sure screening property and the ranking consistency property. Moreover, an iterative version of screening algorithm has also been proposed to accommodate more complex situations. Monte Carlo simulation studies are designed to evaluate the finite sample performance under different model settings. We also illustrate the proposed methods through an empirical analysis.     

Model-free conditional feature screening for ultra-high dimensional right censored data

This paper is concerned with the conditional feature screening for ultra-high dimensional right censored data with some previously identified important predictors. A new model-free conditional feature screening approach, conditional correlation rank sure independence screening, has been proposed and investigated theoretically. The suggested conditional screening procedure has several desirable merits. First, it is model free, and thus robust to model misspecification. Second, it has the advantage of robustness of heavy-tailed distributions of the response and the presence of potential outliers in response. Third, it is naturally applicable to complete data when there is no censoring. Through simulation studies, we demonstrate that the proposed approach outperforms the CoxCS of Hong et al. under some circumstances. A real dataset is used to illustrate the usefulness of the proposed conditional screening method.     

A sure independence screening procedure for ultra-high dimensional partially linear additive models

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 procedure, in the first step, is constructed based on the concept of cumulative distribution function and conditional expectation of response in the framework of marginal correlation. B-splines and empirical distribution functions are used to estimate the two above measures. The sure screening property of this procedure is also established. In the second step, a double penalization based procedure is applied to identify nonzero and linear components, simultaneously. The performance of the designed method is examined by several test functions to show its capabilities against competitor methods when the distribution of errors is varied. Simulation studies imply that the proposed screening procedure can be applied to the ultra-high dimensional data and well detect the influential covariates. It also demonstrate the superiority in comparison with the existing methods. This method is also applied to identify most influential genes for overexpression of a G protein-coupled receptor in mice.     

Efficient three-level screening designs using weighing matrices

Screening is the first stage of many industrial experiments and is used to determine efficiently and effectively a small number of potential factors among a large number of factors which may affect a particular response. In a recent paper, Jones and Nachtsheim [A class of three-level designs for definitive screening in the presence of second-order effects. J. Qual. Technol. 2011;43:1–15] have given a class of three-level designs for screening in the presence of second-order effects using a variant of the coordinate exchange algorithm as it was given by Meyer and Nachtsheim [The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 1995;37:60–69]. Xiao et al. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8] have used conference matrices to construct definitive screening designs with good properties. In this paper, we propose a method for the construction of efficient three-level screening designs based on weighing matrices and their complete foldover. This method can be considered as a generalization of the method proposed by Xiao et al. [Constructing definitive screening designs using conference matrices. J. Qual. Technol. 2012;44:2–8]. Many new orthogonal three-level screening designs are constructed and their properties are explored. These designs are highly D-efficient and provide uncorrelated estimates of main effects that are unbiased by any second-order effect. Our approach is relatively straightforward and no computer search is needed since our designs are constructed using known weighing matrices.     

A New Method for the Analysis of Supersaturated Designs with Discrete Data

Supersaturated designs are factorial designs in which the number of potential effects is greater than the run size. They are commonly used in screening experiments, with the aim of identifying the dominant active factors with low cost. However, an important research field, which is poorly developed, is the analysis of such designs with non-normal response. In this article, we develop a variable selection strategy, through the modification of the PageRank algorithm, which is commonly used in the Google search engine for ranking Webpages. The proposed method incorporates an appropriate information theoretical measure into this algorithm and as a result, it can be efficiently used for factor screening. A noteworthy advantage of this procedure is that it allows the use of supersaturated designs for analyzing discrete data and therefore a generalized linear model is assumed. As it is depicted via a thorough simulation study, in which the Type I and Type II error rates are computed for a wide range of underlying models and designs, the presented approach can be considered quite advantageous and effective.     

New Statistic to Increase Correctness in Simulation Factor Screening Using Frequency Domain Method

Simulation models often include a large number of input factors, many of them may be unimportant to the output; justifying the use of factor screening experiments to eliminate unimportant input factors from consideration in later stages of analysis. With a large number of factors, the challenge is designing experiments so that total number of runs and consequently the required time and cost decrease while achieving a satisfactory detection rate. This article employs frequency domain method (FDM) which is applicable in discrete-event simulation models to propose a new statistic defined as the ratio of estimated signal spectrum to maximum estimated noise spectrum. The proposed method not only has the FDM advantages compared to classic screening approaches but also helps to reduce the error of associated with distinguishing important effects from unimportant ones. Furthermore, as an alternative to the existing statistics, it is shown that not only the proposed statistic does not deteriorate the power of the screening test but in some instances it helps to improve it.     

Model-free slice screening for ultrahigh-dimensional survival data

For ultrahigh-dimensional data, independent feature screening has been demonstrated both theoretically and empirically to be an effective dimension reduction method with low computational demanding. Motivated by the Buckley–James method to accommodate censoring, we propose a fused Kolmogorov–Smirnov filter to screen out the irrelevant dependent variables for ultrahigh-dimensional survival data. The proposed model-free screening method can work with many types of covariates (e.g. continuous, discrete and categorical variables) and is shown to enjoy the sure independent screening property under mild regularity conditions without requiring any moment conditions on covariates. In particular, the proposed procedure can still be powerful when covariates are strongly dependent on each other. We further develop an iterative algorithm to enhance the performance of our method while dealing with the practical situations where some covariates may be marginally unrelated but jointly related to the response. We conduct extensive simulations to evaluate the finite-sample performance of the proposed method, showing that it has favourable exhibition over the existing typical methods. As an illustration, we apply the proposed method to the diffuse large-B-cell lymphoma study.     

Robust rank screening for ultrahigh dimensional discriminant analysis

In this paper, we consider sure independence feature screening for ultrahigh dimensional discriminant analysis. We propose a new method named robust rank screening based on the conditional expectation of the rank of predictor’s samples. We also establish the sure screening property for the proposed procedure under simple assumptions. The new procedure has some additional desirable characters. First, it is robust against heavy-tailed distributions, potential outliers and the sample shortage for some categories. Second, it is model-free without any specification of a regression model and directly applicable to the situation with many categories. Third, it is simple in theoretical derivation due to the boundedness of the resulting statistics. Forth, it is relatively inexpensive in computational cost because of the simple structure of the screening index. Monte Carlo simulations and real data examples are used to demonstrate the finite sample performance.     

An iterative approach to distance correlation-based sure independence screening

Feature screening and variable selection are fundamental in analysis of ultrahigh-dimensional data, which are being collected in diverse scientific fields at relatively low cost. Distance correlation-based sure independence screening (DC-SIS) has been proposed to perform feature screening for ultrahigh-dimensional data. The DC-SIS possesses sure screening property and filters out unimportant predictors in a model-free manner. Like all independence screening methods, however, it fails to detect the truly important predictors which are marginally independent of the response variable due to correlations among predictors. When there are many irrelevant predictors which are highly correlated with some strongly active predictors, the independence screening may miss other active predictors with relatively weak marginal signals. To improve the performance of DC-SIS, we introduce an effective iterative procedure based on distance correlation to detect all truly important predictors and potentially interactions in both linear and nonlinear models. Thus, the proposed iterative method possesses the favourable model-free and robust properties. We further illustrate its excellent finite-sample performance through comprehensive simulation studies and an empirical analysis of the rat eye expression data set.     

Robust feature screening for high-dimensional survival data

Ultra-high dimensional data arise in many fields of modern science, such as medical science, economics, genomics and imaging processing, and pose unprecedented challenge for statistical analysis. With such rapid-growth size of scientific data in various disciplines, feature screening becomes a primary step to reduce the high dimensionality to a moderate scale that can be handled by the existing penalized methods. In this paper, we introduce a simple and robust feature screening method without any model assumption to tackle high dimensional censored data. The proposed method is model-free and hence applicable to a general class of survival models. The sure screening and ranking consistency properties without any finite moment condition of the predictors and the response are established. The computation of the proposed method is rather straightforward. Finite sample performance of the newly proposed method is examined via extensive simulation studies. An application is illustrated with the gene association study of the mantle cell lymphoma.     

A model-free feature screening approach based on kernel density estimation

In this article, a new model-free feature screening method named after probability density (mass) function distance (PDFD) correlation is presented for ultrahigh-dimensional data analysis. We improve the fused-Kolmogorov filter (F-KOL) screening procedure through probability density distribution. The proposed method is also fully nonparametric and can be applied to more general types of predictors and responses, including discrete and continuous random variables. Kernel density estimate method and numerical integration are applied to obtain the estimator we proposed. The results of simulation studies indicate that the fused-PDFD performs better than other existing screening methods, such as F-KOL filter, sure-independent screening (SIS), sure independent ranking and screening (SIRS), distance correlation sure-independent screening (DCSIS) and robust ranking correlation screening (RRCS). Finally, we demonstrate the validity of fused-PDFD by a real data example.     

Stable feature screening for ultrahigh dimensional data

This paper is concerned with the stable feature screening for the ultrahigh dimensional data. To deal with the ultrahigh dimensional data problem and screen the important features, a set-averaging measurement is proposed. The model averaging technique and the conditional quantile method are used to construct the weighted set-averaging feature screening procedure to identify the relationships between the possible predictors and the response variable. The proposed screening method is model free, stable and possesses the sure screening property under some regular conditions. Some Monte Carlo simulations and a real data application are conducted to evaluate the performance of the proposed procedure.     

A robust variable screening method for high-dimensional data

In practice, the presence of influential observations may lead to misleading results in variable screening problems. We, therefore, propose a robust variable screening procedure for high-dimensional data analysis in this paper. Our method consists of two steps. The first step is to define a new high-dimensional influence measure and propose a novel influence diagnostic procedure to remove those unusual observations. The second step is to utilize the sure independence screening procedure based on distance correlation to select important variables in high-dimensional regression analysis. The new influence measure and diagnostic procedure that we developed are model free. To confirm the effectiveness of the proposed method, we conduct simulation studies and a real-life data analysis to illustrate the merits of the proposed approach over some competing methods. Both the simulation results and the real-life data analysis demonstrate that the proposed method can greatly control the adverse effect after detecting and removing those unusual observations, and performs better than the competing methods.     

On correlation rank screening for ultra-high dimensional competing risks data

In recent years, numerous feature screening schemes have been developed for ultra-high dimensional standard survival data with only one failure event. Nevertheless, existing literature pays little attention to related investigations for competing risks data, in which subjects suffer from multiple mutually exclusive failures. In this article, we develop a new marginal feature screening for ultra-high dimensional time-to-event data to allow for competing risks. The proposed procedure is model-free, and robust against heavy-tailed distributions and potential outliers for time to the type of failure of interest. Apart from this, it is invariant to any monotone transformation of event time of interest. Under rather mild assumptions, it is shown that the newly suggested approach possesses the ranking consistency and sure independence screening properties. Some numerical studies are conducted to evaluate the finite-sample performance of our method and make a comparison with its competitor, while an application to a real data set is provided to serve as an illustration.     

基于信息可替代性的评价指标筛选研究

提出一种指标筛选方法,旨在筛选出对评价结果影响显著、反映信息重叠程度低的评价指标。以相对离散系数作为指标的信息含量,依据提出的累计信息贡献率标准删除信息含量明显偏小的指标进行指标的初筛,克服现有研究仅利用相对离散系数进行指标筛选的不足。借鉴聚类分析的思想,取初筛后保留下来的一个指标与其余各指标构成Person相关系数平方的均值,反映该指标的信息可被其余全部指标替代的程度。通过信息可替代性标准剔除信息可替代性较大的指标,保证最终被保留的指标间反映的信息重叠程度低,克服现有研究仅通过两个指标间的相关性筛选指标难以有效降低评价指标集信息重叠的不足。此外,针对剔除信息重叠的指标与剔除对评价结果影响不显著的指标何者优先为宜的问题,提出了显著再相关的指标筛选标准。最后,通过一个实例说明指标筛选方法的可行性。     

Quantile-adaptive variable screening in ultra-high dimensional varying coefficient models

The varying-coefficient model is an important nonparametric statistical model since it allows appreciable flexibility on the structure of fitted model. For ultra-high dimensional heterogeneous data it is very necessary to examine how the effects of covariates vary with exposure variables at different quantile level of interest. In this paper, we extended the marginal screening methods to examine and select variables by ranking a measure of nonparametric marginal contributions of each covariate given the exposure variable. Spline approximations are employed to model marginal effects and select the set of active variables in quantile-adaptive framework. This ensures the sure screening property in quantile-adaptive varying-coefficient model. Numerical studies demonstrate that the proposed procedure works well for heteroscedastic data.     

A method for analyzing supersaturated designs inspired by control charts

The identification of active effects in supersaturated designs (SSDs) constitutes a problem of considerable interest to both scientists and engineers. The complicated structure of the design matrix renders the analysis of such designs a complicated issue. Although several methods have been proposed so far, a solution to the problem beyond one or two active factors seems to be inadequate. This article presents a heuristic approach for analyzing SSDs using the cumulative sum control chart (CUSUM) under a sure independence screening approach. Simulations are used to investigate the performance of the method comparing the proposed method with other well-known methods from the literature. The results establish the powerfulness of the proposed methodology.     

Variable screening for survival data in the presence of heterogeneous censoring

Variable screening for censored survival data is most challenging when both survival and censoring times are correlated with an ultrahigh-dimensional vector of covariates. Existing approaches to handling censoring often make use of inverse probability weighting by assuming independent censoring with both survival time and covariates. This is a convenient but rather restrictive assumption which may be unmet in real applications, especially when the censoring mechanism is complex and the number of covariates is large. To accommodate heterogeneous (covariate-dependent) censoring that is often present in high-dimensional survival data, we propose a Gehan-type rank screening method to select features that are relevant to the survival time. The method is invariant to monotone transformations of the response and of the predictors, and works robustly for a general class of survival models. We establish the sure screening property of the proposed methodology. Simulation studies and a lymphoma data analysis demonstrate its favorable performance and practical utility.