Feature Screening via Distance Correlation Learning

By Runze Li, Wei Zhong, Liping Zhu. 2012

807 citations recorded by the source corpus.

This article 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 correlation (DC-SIS). The DC-SIS can be implemented as easily as the sure independence screening (SIS) procedure based on the Pearson correlation proposed by Fan and Lv. However, the DC-SIS can significantly improve the SIS. Fan and Lv established the sure screening property for the SIS based on linear models, but the sure screening property is valid for the DC-SIS under more general settings, including linear models. Furthermore, the implementation of the DC-SIS does not require model specification (e.g., linear model or generalized linear model) for responses or predictors. This is a very appealing property in ultrahigh-dimensional data analysis. Moreover, the DC-SIS can be used directly to screen grouped predictor variables and multivariate response variables. We establish the sure screening property for the DC-SIS, and conduct simulations to examine its finite sample performance. A numerical comparison indicates that the DC-SIS performs much better than the SIS in various models. We also illustrate the DC-SIS through a real-data example.

Subfields: Epidemiology, Infectious Diseases, Public Health, Environmental and Occupational Health

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Citations in the corpus

Supervised Dimensionality Reduction via Distance Correlation Maximization (2016, methodology): “To further add, other works of Li et al. [2012], Kong et al. [2015], Berrendero et al. [2014] have used Distance Correlation as a criterion for feature selection in a regression setting.”
An Updated Literature Review of Distance Correlation and Its Applications to Time Series (2017, neutral): “Li et al. (2012) show the sure screening property for DC-SIS, under moderate assumptions, and show that this method accommodates linear models as a special case.”
Fast Computing for Distance Covariance (2014, methodology): “The following description follows the one in Li et al. (2012). We generate x = (X1,X2, .”
Partial martingale difference correlation (2015, neutral): “To measure the dependence of two random vectors X ∈ Rp and Y ∈ Rq, Székely, Rizzo and Bakirov [13] proposed distance covariance (dCov) and distance correlation (dCor), which have attracted a lot of attention lately; see related work by Sźekely and Rizzo [12], Li, Zhong and Zhu [7], Kong et al.…”
R EDUCING LEAKAGE IN DISTRIBUTED DEEP LEARNING FOR SENSITIVE HEALTH DATA (2019, methodology): “Distance correlation has been used in recent non-deep learning applications including causal inference Liu & Chan (2016), sureindependence screening Li et al. (2012), hypothesis testing Sejdinovic et al. (2013), supervised dimensionality reduction Vepakomma et al. (2018b) and embeddings of…”
Energy statistics: A class of statistics based on distances (2013, methodology): “Li, Zhong, and Zhu [28] applied distance correlation for feature screening for ultra-high dimensional data.”
A fast algorithm for computing distance correlation (2018, methodology): “Our algorithm will speed up any computational technique that depends on the calculation of univariate distance covariance for example, feature screening (Li et al., 2012).”
A Statistically and Numerically Efficient Independence Test Based on Random Projections and Distance Covariance (2017, methodology): “Distance-based independence/dependence measurements sometimes have been utilized in performing a greedy feature selection, often via dependence maximization [8,30,31], and it has been effective on some real-world datasets.”
High dimensional ordinary least squares projection for screening variables (2015, methodology): “Our example is taken from Meinshausen and Bühlmann (2010) and Cho and Fryzlewicz (2012).”
Partial Distance Correlation with Methods for Dissimilarities (2013, neutral): “Properties, extensions and applications of distance correlation have been discussed in the recent literature; see, for example, Dueck et al. [4], Lyons [16], Kong et al. [12] and Li, Zhong and Zhu [15].”
Challenges of Big Data Analysis (2013, positive): “In addition, the authors of [91] utilized the distance correlation to conduct screening, [92] employed rank correlation and [28] proposed an iteratively screening and selection method.”