Model-free feature screening for ultrahigh-dimensional data conditional on some variables

In this paper, the conditional distance correlation (CDC) is used as a measure of correlation to develop a conditional feature screening procedure given some significant variables for ultrahigh-dimensional data. The proposed procedure is model free and is called conditional distance correlation-sure independence screening (CDC-SIS for short). That is, we do not specify any model structure between the response and the predictors, which is appealing in some practical problems of ultrahigh-dimensional data analysis. The sure screening property of the CDC-SIS is proved and a simulation study was conducted to evaluate the finite sample performances. Real data analysis is used to illustrate the proposed method. The results indicate that CDC-SIS performs well.     

Conditional-quantile screening for ultrahigh-dimensional survival data via martingale difference correlation

Using the so-called martingale difference correlation (MDC), we propose a novel censored-conditional-quantile screening approach for ultrahigh-dimensional survival data with heterogeneity (which is often present in such data). By incorporating a weighting scheme, this method is a natural extension of MDC-based conditional quantile screening, as considered in Shao and Zhang (2014), to handle ultrahigh-dimensional survival data. The proposed screening procedure has a sure-screening property under certain technical conditions and an excellent capability of detecting the nonlinear relationship between independent and censored dependent variables. Both simulation results and an analysis of real data demonstrate the effectiveness of the new censored conditional quantile-screening procedure.     

Conditional distance correlation screening for sparse ultrahigh-dimensional models

This paper is concerned with feature screening for ultrahigh-dimensional covariates under general varying-coefficient models. With the sparsity principle and based on the conditional distance correlation, we develop a new marginal feature screening procedure called CDC-SIS to select significant covariates and show that it possesses the sure screening property and ranking consistency property under some regularity conditions. The proposed procedure enjoys two appealing merits. First, the model we considered is more flexible than traditional varying-coefficients regression models, so the method can be used in a wider range of applications. Second, CDC-SIS can be used directly to deal with grouped predictor variables and multivariate responses. We assess the finite sample properties of the proposed procedure by Monte Carlo studies, and illustrate our method by an empirical analysis of a real data set. Compared with other similar works, our procedure yields better performance.     

Model-free feature screening for high-dimensional survival data

With the rapid-growth-in-size scientific data in various disciplines, feature screening plays an important role to reduce the high-dimensionality to a moderate scale in many scientific fields. In this paper, we introduce a unified and robust model-free feature screening approach for high-dimensional survival data with censoring, which has several advantages: it is a model-free approach under a general model framework, and hence avoids the complication to specify an actual model form with huge number of candidate variables; under mild conditions without requiring the existence of any moment of the response, it enjoys the ranking consistency and sure screening properties in ultra-high dimension. In particular, we impose a conditional independence assumption of the response and the censoring variable given each covariate, instead of assuming the censoring variable is independent of the response and the covariates. Moreover, we also propose a more robust variant to the new procedure, which possesses desirable theoretical properties without any finite moment condition of the predictors and the response. The computation of the newly proposed methods does not require any complicated numerical optimization and it is fast and easy to implement. Extensive numerical studies demonstrate that the proposed methods perform competitively for various configurations. Application is illustrated with an analysis of a genetic data set.     

Model-free conditional independence feature screening for ultrahigh dimensional data

Feature screening plays an important role in ultrahigh dimensional data analysis. This paper is concerned with conditional feature screening when one is interested in detecting the association between the response and ultrahigh dimensional predictors (e.g., genetic makers) given a low-dimensional exposure variable (such as clinical variables or environmental variables). To this end, we first propose a new index to measure conditional independence, and further develop a conditional screening procedure based on the newly proposed index. We systematically study the theoretical property of the proposed procedure and establish the sure screening and ranking consistency properties under some very mild conditions. The newly proposed screening procedure enjoys some appealing properties. (a) It is model-free in that its implementation does not require a specification on the model structure; (b) it is robust to heavy-tailed distributions or outliers in both directions of response and predictors; and (c) it can deal with both feature screening and the conditional screening in a unified way. We study the finite sample performance of the proposed procedure by Monte Carlo simulations and further illustrate the proposed method through two real data examples.     

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.     

Tournament screening cum EBIC for feature selection with high-dimensional feature spaces

The feature selection characterized by relatively small sample size and extremely high-dimensional feature space is common in many areas of contemporary statistics. The high dimensionality of the feature space causes serious difficulties: (i) the sample correlations between features become high even if the features are stochastically independent; (ii) the computation becomes intractable. These difficulties make conventional approaches either inapplicable or inefficient. The reduction of dimensionality of the feature space followed by low dimensional approaches appears the only feasible way to tackle the problem. Along this line, we develop in this article a tournament screening cum EBIC approach for feature selection with high dimensional feature space. The procedure of tournament screening mimics that of a tournament. It is shown theoretically that the tournament screening has the sure screening property, a necessary property which should be satisfied by any valid screening procedure. It is demonstrated by numerical studies that the tournament screening cum EBIC approach enjoys desirable properties such as having higher positive selection rate and lower false discovery rate than other approaches. Zehua Chen was supported by Singapore Ministry of Educations ACRF Tier 1 (Grant No. R-155-000-065-112). Jiahua Chen was supported by the National Science and Engineering Research Countil of Canada and MITACS, Canada.     

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.     

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.     

A hybrid deep computation model for feature learning on aero-engine data: applications to fault detection

Recently, the safety of aircraft has attracted much attention with some crashes occurring. Gas-path faults, as the most common faults of aircraft, pose a vast challenge for the safety of aircraft because of the complexity of the aero-engine structure. In this article, a hybrid deep computation model is proposed to effectively detect gas-path faults on the basis of the performance data. In detail, to capture the local spatial features of the gas-path performance data, an unfully connected convolutional neural network of one-dimensional kernels is used. Furthermore, to model the temporal patterns hidden in the gas-path faults, a recurrent computation architecture is introduced. Finally, extensive experiments are conducted on real aero-engine data. The results show that the proposed model can outperform the models with which it is compared.     

Framework for efficient feature selection in genetic algorithm based data mining

We present the design of more effective and efficient genetic algorithm based data mining techniques that use the concepts of feature selection. Explicit feature selection is traditionally done as a wrapper approach where every candidate feature subset is evaluated by executing the data mining algorithm on that subset. In this article we present a GA for doing both the tasks of mining and feature selection simultaneously by evolving a binary code along side the chromosome structure used for evolving the rules. We then present a wrapper approach to feature selection based on Hausdorff distance measure. Results from applying the above techniques to a real world data mining problem show that combining both the feature selection methods provides the best performance in terms of prediction accuracy and computational efficiency.     

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.     

Genetic programming for feature construction and selection in classification on high-dimensional data

Classification on high-dimensional data with thousands to tens of thousands of dimensions is a challenging task due to the high dimensionality and the quality of the feature set. The problem can be addressed by using feature selection to choose only informative features or feature construction to create new high-level features. Genetic programming (GP) using a tree-based representation can be used for both feature construction and implicit feature selection. This work presents a comprehensive study to investigate the use of GP for feature construction and selection on high-dimensional classification problems. Different combinations of the constructed and/or selected features are tested and compared on seven high-dimensional gene expression problems, and different classification algorithms are used to evaluate their performance. The results show that the constructed and/or selected feature sets can significantly reduce the dimensionality and maintain or even increase the classification accuracy in most cases. The cases with overfitting occurred are analysed via the distribution of features. Further analysis is also performed to show why the constructed feature can achieve promising classification performance.     

A geometric feature for finite element schemes

In this note we characterize the geometric feature of a (μ;r,k)—FES. Namely, for a C^μ triangular interpolation scheme with C^r vertex data, any angle of the macrotriangle must be divided into at least (μ+1)/(r+1−μ) parts.     

Ensemble feature selection for high dimensional data: a new method and a comparative study

The curse of dimensionality is based on the fact that high dimensional data is often difficult to work with. A large number of features can increase the noise of the data and thus the error of a learning algorithm. Feature selection is a solution for such problems where there is a need to reduce the data dimensionality. Different feature selection algorithms may yield feature subsets that can be considered local optima in the space of feature subsets. Ensemble feature selection combines independent feature subsets and might give a better approximation to the optimal subset of features. We propose an ensemble feature selection approach based on feature selectors’ reliability assessment. It aims at providing a unique and stable feature selection without ignoring the predictive accuracy aspect. A classification algorithm is used as an evaluator to assign a confidence to features selected by ensemble members based on their associated classification performance. We compare our proposed approach to several existing techniques and to individual feature selection algorithms. Results show that our approach often improves classification performance and feature selection stability for high dimensional data sets.     

A screening method for a nonparametric model

In this paper a class of estimators of a screening threshold in a nonparametric positive dependence model is introduced and the strong consistency of its members is investigated.     

A certain feature of logarithmic spirals

A curve formed by inversion of a logarithmic spiral is called a double logarithmic spiral. The curves in this family possess the following property: there always exists such a spiral with continuous and monotone curvature satisfying any possible boundary conditions (endpoints, tangents, and curvatures). The problem of constructing a spiral with continuous curvature and prescribed curvature elements at the endpoints is thus solved. Bibliography: 6 titles.     

Panel data models with cross-sectional dependence: a selective review

In this review, we highlight some recent methodological and theoretical developments in estimation and testing of large panel data models with cross-sectional dependence. The paper begins with a discussion of issues of cross-sectional dependence, and introduces the concepts of weak and strong cross-sectional dependence. Then, the main attention is primarily paid to spatial and factor approaches for modeling cross-sectional dependence for both linear and nonlinear (nonparametric and semiparametric) panel data models. Finally, we conclude with some speculations on future research directions.