screenIID {VariableScreening}

Feature Selection for Ultrahigh-Dimensional Datasets with Independent Subjects,

Description

Implements one of three screening procedures: Sure Independent Ranking and Screening (SIRS), Distance Correlation Sure Independence Screening (DC-SIS), or MV Sure Independence Screening (MV-SIS). In general they are extensions of the sure independence screening concept proposed by Fan and Lv (2008), but without a parametric assumption (e.g., linear or logistic) on the relationship between the predictor variables X and outcome Y.

Screening methods each rank the predictors based on some measure of their estimated strength of relationship with Y. The assumption is that only a few among the top-ranked variables are likely to be truly significant predictors.

The original version of SIS involved ranking the predictors by their correlation with Y, implying a linear relationship. The SIRS method is an extension proposed by Zhu, Li, Li, & Zhu (2011), which involved ranking the predictors by their correlation with the rank-ordered Y instead, thereby not assuming a linear correlation, and potentially outperforming SIS.

DC-SIS was then proposed by Li, Zhong and Zhu (2012) and its relationship measure is the distance correlation (DC) between a covariate and the outcome, a nonparametric generalization of the correlation coefficient (Szekely, Rizzo, & Bakirov, 2007). The function uses the dcor function from the R package energy in order to calculate this correlation. Simulations showed that DC-SIS could sometimes provide a further advantage over SIRS.

The above measures were primarily intended for a numerical Y. Cui, Li, and Zhong (2015) proposed MV-SIS, which was developed for categorical Y (including binary Y) as in discriminant analysis, and which is also robust to heavy-tailed predictor distributions. The measure used by MV-SIS for the association strength between a particular Xk and Y is a mean conditional variance measure called MV for short, namely the expectation in X of the variance in Y of the conditional cumulative distribution function F(x|Y)=P(X<=x|Y); note that like the correlation or distance correlation, this is zero if X and Y are independent because F(x) does not depend on Y in that case. Cui, Li, and Zhong (2015) also point out that the MV-SIS can alternatively be used with categorical X variables and numerical Y, instead of numerical X and categorical Y. This function supports that option as "MV-SIS-NY."

Whichever option is chosen, the function returns the ranking of the predictors according to the appropriate association measure.

The function code is adapted from the relevant authors' code. Special thanks are due to Wei Zhong for providing some of the code upon which this function is based.

Usage

screenIID(X, Y, method = "DC-SIS")

Arguments

X

Matrix of predictors to be screened. There should be one row for each observation.

Y

Vector of responses. It should have the same length as the number of rows of X. The responses should be numerical if SIRS or DC-SIS is used. The responses should be integers representing response categories if MV-SIS is used. Binary responses can be used for any method.

method

Screening method. The options are "SIRS", "DC-SIS", "MV-SIS" and "MV-SIS-NY", as described above.

Value

A list with following components:

measurement A vector of length equal to the number of columns in the input matrix X. It contains estimated strength of relationship with Y rank The rank of the error measures. This will have length equal to the number of columns in the input matrix X, and will consist of a permutation of the integers 1 through that length. A rank of 1 indicates the feature which appears to have the best predictive performance, 2 represents the second best and so on.

References

Cui, H., Li, R., & Zhong, W. (2015). Model-free feature screening for ultrahigh dimensional discriminant analysis. Journal of the American Statistical Association, 110: 630-641. <DOI:10.1080/01621459.2014.920256>

Fan, J., & Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society, B, 70: 849-911. <DOI:10.1111/j.1467-9868.2008.00674.x>

Li, R., zhong, W., & Zhu, L. (2012). Feature screening via distance correlation learning. Journal of the American Statistical Association, 107: 1129-1139. <DOI:10.1080/01621459.2012.695654>

Szekely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and Testing Dependence by Correlation of Distances. Annals of Statistics, 35, 2769-2794. <DOI: 10.1214/009053607000000505>

Zhu, L.-P., Li, L., Li, R., & Zhu, L.-X. (2011) Model-free feature screening for ultrahigh-dimensional data. Journal of the American Statistical Association, 106: 1464-1475. <DOI:10.1198/jasa.2011.tm10563>

Examples

set.seed(12345678)
results <- simulateDCSIS(n=100,p=500)
rank<- screenIID(X = results$X, Y = results$Y, method="DC-SIS")