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Nonparametric Feature Screening via the Variance of the Regression Function
Department of Mathematics, Milwaukee School of Engineering, Milwaukee, USA
Department of Statistics, Pennsylvania State University, University Park, USA
- 1 Department of Mathematics, Milwaukee School of Engineering, Milwaukee, USA
- 2 Department of Statistics, Pennsylvania State University, University Park, USA
Open Journal of Statistics·Volume 14 (2024)·Pages 413–438·Published 26 August 2024·DOI10.4236/ojs.2024.144017
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Abstract
This article develops a procedure for screening variables, in ultra high-di- mensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their respective marginal regression functions (RV-SIS). We show that, under some mild technical conditions, the RV-SIS possesses a sure screening property, which is defined by Fan and Lv (2008). Numerical comparisons suggest that RV-SIS has competitive performance compared to other screening procedures, and outperforms them in many different model settings.
KeywordsSure Independence ScreeningNonparametric RegressionUltrahigh-Dimensional DataVariable Selection
- Fan, J.Q., Samworth, R. and Wu, Y.C. (2009) Ultrahigh Dimensional Feature Selection: BEYOND the linear Model. The Journal of Machine Learning Research , 10, 2013-2038.
- Fan, J. and Lv, J. (2008) Sure Independence Screening for Ultrahigh Dimensional Feature Space. Journal of the Royal Statistical Society Series B : Statistical Methodology , 70, 849-911. https://doi.org/10.1111/j.1467-9868.2008.00674.x
- Fan, J., Feng, Y. and Song, R. (2011) Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models. Journal of the American Statistical Association , 106, 544-557. https://doi.org/10.1198/jasa.2011.tm09779
- Li, R., Zhong, W. and Zhu, L. (2012) Feature Screening via Distance Correlation Learning. Journal of the American Statistical Association , 107, 1129-1139. https://doi.org/10.1080/01621459.2012.695654
- Li, G.R., Peng, H., Zhang, J., Zhu, L.X., et al . (2014) Robust Rank Correlation Based Screening. The Annals of Statistics , 40, 1846-1877.
- Wang, Z. and Deng, G. (2022) Model-Free Feature Screening Based on Gini Impurity for Ultrahigh-Dimensional Multiclass Classification. Open Journal of Statistics , 12, 711-732. https://doi.org/10.4236/ojs.2022.125042
- Chen, T. and Deng, G. (2023) Model-free Feature Screening via Maximal Information Coefficient (MIC) for Ultrahigh-Dimensional Multiclass Classification. Open Journal of Statistics , 13, 917-940. https://doi.org/10.4236/ojs.2023.136046
- Wang, L., Akritas, M.G. and Van Keilegom, I. (2008) An Anova-Type Nonparametric Diagnostic Test for Heteroscedastic Regression Models. Journal of Nonparametric Statistics , 20, 365-382. https://doi.org/10.1080/10485250802066112
- Zhu, L., Li, L., Li, R. and Zhu, L. (2011) Model-Free Feature Screening for Ultrahigh-Dimensional Data. Journal of the American Statistical Association , 106, 1464-1475. https://doi.org/10.1198/jasa.2011.tm10563
- Segal, M.R., Dahlquist, K.D. and Conklin, B.R. (2003) Regression Approaches for Microarray Data Analysis. Journal of Computational Biology , 10, 961-980. https://doi.org/10.1089/106652703322756177
- Doksum, K. and Samarov, A. (1995) Nonparametric Estimation of Global Functionals and a Measure of the Explanatory Power of Covariates in Regression. The Annals of Statistics , 23, 1443-1473. https://doi.org/10.1214/aos/1176324307
- Kim, D., Li, R., Dudek, S.M., Frase, A.T., Pendergrass, S.A. and Ritchie, M.D. (2014) Knowledge-Driven Genomic Interactions: An Application in Ovarian Cancer. BioData Mining , 7, Article No. 20. https://doi.org/10.1186/1756-0381-7-20