Censored Composite Conditional Quantile Screening for High-Dimensional Survival Data

In this paper,we introduce the censored composite conditional quantile coefficient(cC-CQC)to rank the relative importance of each predictor in high-dimensional censored regression.The cCCQC takes advantage of all useful information across quantiles and can detect nonlinear effects including interactions and heterogeneity,effectively.Furthermore,the proposed screening method based on cCCQC is robust to the existence of outliers and enjoys the sure screening property.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors,particularly when the variables are highly correlated.

Feature selection of ultrahigh-dimensional covariates with survival outcomes:a selective review

Many modern biomedical studies have yielded survival data with high-throughput predictors.The goals of scientific research often lie in identifying predictive biomarkers,understanding biological mechanisms and making accurate and precise predictions.Variable screening is a crucial first step in achieving these goals.This work conducts a selective review of feature screening procedures for survival data with ultrahigh dimensional covariates.We present the main methodologies,along with the key conditions that ensure sure screening properties.The practical utility of these methods is examined via extensive simulations.We conclude the review with some future opportunities in this field.

A selective overview of feature screening for ultrahigh-dimensional data

High-dimensional data have frequently been collected in many scientific areas including genomewide association study, biomedical imaging, tomography, tumor classifications, and finance. Analysis of highdimensional data poses many challenges for statisticians. Feature selection and variable selection are fundamental for high-dimensional data analysis. The sparsity principle, which assumes that only a small number of predictors contribute to the response, is frequently adopted and deemed useful in the analysis of high-dimensional data.Following this general principle, a large number of variable selection approaches via penalized least squares or likelihood have been developed in the recent literature to estimate a sparse model and select significant variables simultaneously. While the penalized variable selection methods have been successfully applied in many highdimensional analyses, modern applications in areas such as genomics and proteomics push the dimensionality of data to an even larger scale, where the dimension of data may grow exponentially with the sample size. This has been called ultrahigh-dimensional data in the literature. This work aims to present a selective overview of feature screening procedures for ultrahigh-dimensional data. We focus on insights into how to construct marginal utilities for feature screening on specific models and motivation for the need of model-free feature screening procedures.

Robust Sure Independence Screening for Ultrahigh Dimensional Non-normal Data

Sure independence screening（SIS） has been proposed to reduce the ultrahigh dimensionality down to a moderate scale and proved to enjoy the sure screening property under Gaussian linear models.However,the observed response is often skewed or heavy-tailed with extreme values in practice,which may dramatically deteriorate the performance of SIS.To this end,we propose a new robust sure independence screening（RoSIS） via considering the correlation between each predictor and the distribution function of the response.The proposed approach contributes to the literature in the following three folds： First,it is able to reduce ultrahigh dimensionality effectively.Second,it is robust to heavy tails or extreme values in the response.Third,it possesses both sure screening property and ranking consistency property under milder conditions.Furthermore,we demonstrate its excellent finite sample performance through numerical simulations and a real data example.

Stable correlation and robust feature screening

In this paper,we propose a new correlation,called stable correlation,to measure the dependence between two random vectors.The new correlation is well defined without the moment condition and is zero if and only if the two random vectors are independent.We also study its other theoretical properties.Based on the new correlation,we further propose a robust model-free feature screening procedure for ultrahigh dimensional data and establish its sure screening property and rank consistency property without imposing the subexponential or sub-Gaussian tail condition,which is commonly required in the literature of feature screening.We also examine the finite sample performance of the proposed robust feature screening procedure via Monte Carlo simulation studies and illustrate the proposed procedure by a real data example.

Group screening for ultra-high-dimensional feature under linear model

Ultra-high-dimensional data with grouping structures arise naturally in many contemporary statistical problems,such as gene-wide association studies and the multi-factor analysis-of-variance(ANOVA).To address this issue,we proposed a group screening method to do variables selection on groups of variables in linear models.This group screening method is based on a working independence,and sure screening property is also established for our approach.To enhance the finite sample performance,a data-driven thresholding and a two-stage iterative procedure are developed.To the best of our knowledge,screening for grouped variables rarely appeared in the literature,and this method can be regarded as an important and non-trivial extension of screening for individual variables.An extensive simulation study and a real data analysis demonstrate its finite sample performance.

Sure feature screening for high-dimensional dichotomous classification

The curse of high-dimensionality has emerged in the statistical fields more and more frequently.Many techniques have been developed to address this challenge for classification problems. We propose a novel feature screening procedure for dichotomous response data. This new method can be implemented as easily as t-test marginal screening approach, and the proposed procedure is free of any subexponential tail probability conditions and moment requirement and not restricted in a specific model structure. We prove that our method possesses the sure screening property and also illustrate the effect of screening by Monte Carlo simulation and apply it to a real data example.

Feature Screening for High-Dimensional Survival Data via Censored Quantile Correlation

This paper proposes a new sure independence screening procedure for high-dimensional survival data based on censored quantile correlation(CQC).This framework has two distinctive features:1)Via incorporating a weighting scheme,our metric is a natural extension of quantile correlation(QC),considered by Li(2015),to handle high-dimensional survival data;2)The proposed method not only is robust against outliers,but also can discover the nonlinear relationship between independent variables and censored dependent variable.Additionally,the proposed method enjoys the sure screening property under certain technical conditions.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors.

Sequential profile Lasso for ultra-high-dimensional partially linear models

In this paper, we study ultra-high-dimensional partially linear models when the dimension of thelinear predictors grows exponentially with the sample size. For the variable screening, we proposea sequential profile Lasso method (SPLasso) and show that it possesses the screening property.SPLasso can also detect all relevant predictors with probability tending to one, no matter whetherthe ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a realdata example to assess the performance of the proposed method and compare with the existingmethod.

Influence of co-solvent hydroxyl group number on properties of water-based conductive carbon pastes

A series of water-based conductive carbon pastes were prepared by wet ball milling, followed by vacuum defoaming using isopropyl alcohol, propylene glycol or glycerin as co-solvents. Screen printing was then used to prepare conductive patterns. To determine the influence of co-solvent hydroxyl group number on the properties of water-based conductive carbon pastes, the rheological properties of the pastes and the surface morphologies and conductivities of the printed patterns were characterized. The results show that paste viscosity increased with the number of hydroxyl groups and the latter also affected thixotropy. In addition, the boiling points and surface tensions of the co-solvents increased consistently with hydroxyl group number, affecting the hydrodynamic flow. The conductive carbon paste created using propylene glycol as a co-solvent was the best for screen printing because of its weak coffee-ring effect and appro- priate rheological properties, resulting in a smooth coating surface and uniform deposition of the fillers. The resistivity of the pattern printed using paste PG, containing the closest packing of conductive carbon black particles, was 0.44 Ω cm.