Sparse kernel sufficient dimension reduction

References

• Amini, A.A., and Wainwright, M.J. (2008), ‘High-Dimensional Analysis of Semidefinite Relaxations for Sparse Principal Components’, in Information Theory, 2008. ISIT 2008. IEEE International Symposium on, IEEE, pp. 2454–2458.
   Google Scholar
• Baker, C.R. (1973), ‘Joint Measures and Cross-Covariance Operators’, Transactions of the American Mathematical Society, 186, 273–289.
   Web of Science ®Google Scholar
• Begue, B., Verdier, J., Rieux-Laucat, F., Goulet, O., Morali, A., Canioni, D., Hugot, J.-P., Daussy, C., Verkarre, V., Pigneur, B., and Fischer, A. (2011), ‘Defective Il10 Signaling Defining a Subgroup of Patients with Inflammatory Bowel Disease’, Official Journal of the American College of Gastroenterology ACG, 106(8), 1544–1555.
   PubMed Web of Science ®Google Scholar
• Bondell, H.D., and Li, L. (2009), ‘Shrinkage Inverse Regression Estimation for Model-free Variable Selection’, Journal of the Royal Statistical Society Series B: Statistical Methodology, 71(1), 287–299.
   Google Scholar
• Buisine, M., Desreumaux, P., Leteurtre, E., Copin, M., Colombel, J., Porchet, N., and Aubert, J. (2001), ‘Mucin Gene Expression in Intestinal Epithelial Cells in Crohn's Disease’, Gut, 49(4), 544–551.
   PubMed Web of Science ®Google Scholar
• Chen, X., Zou, C., and Cook, R.D. (2010), ‘Coordinate-independent Sparse Sufficient Dimension Reduction and Variable Selection’, The Annals of Statistics, 38(6), 3696–3723.
   Web of Science ®Google Scholar
• Cook, R.D., and Weisberg, S. (1991), ‘Comment’, Journal of the American Statistical Association, 86(414), 328–332.
   Web of Science ®Google Scholar
• d'Aspremont, A., Ghaoui, L.E., Jordan, M.I., and Lanckriet, G.R. (2005), ‘A Direct Formulation for Sparse PCA Using Semidefinite Programming’, in Advances in Neural Information Processing Systems, pp. 41–48.
   Google Scholar
• Fan, J., and Li, R. (2001), ‘Variable Selection Via Nonconcave Penalized Likelihood and Its Oracle Properties’, Journal of the American Statistical Association, 96(456), 1348–1360.
   Web of Science ®Google Scholar
• Fan, J., Xue, L., and Yao, J. (2017), ‘Sufficient Forecasting Using Factor Models’, Journal of Econometrics, 201(2), 292–306.
   PubMed Web of Science ®Google Scholar
• Fan, J., Xue, L., and Zou, H. (2014), ‘Strong Oracle Optimality of Folded Concave Penalized Estimation’, The Annals of Statistics, 42(3), 819–849.
   PubMed Web of Science ®Google Scholar
• Frommlet, F., and Nuel, G. (2016), ‘An Adaptive Ridge Procedure for L 0 Regularization’, PloS One, 11(2), e0148620.
   PubMed Web of Science ®Google Scholar
• Fukumizu, K., Bach, F.R., and Jordan, M.I. (2009), ‘Kernel Dimension Reduction in Regression’, The Annals of Statistics, 37(4), 1871–1905.
   Web of Science ®Google Scholar
• Jiang, B., Lin, T., Ma, S., and Zhang, S. (2019), ‘Structured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity Analysis’, Computational Optimization and Applications, 72(1), 115–157.
   Web of Science ®Google Scholar
• Li, K.-C. (1991), ‘Sliced Inverse Regression for Dimension Reduction’, Journal of the American Statistical Association, 86(414), 316–327.
   Web of Science ®Google Scholar
• Li, L. (2007), ‘Sparse Sufficient Dimension Reduction’, Biometrika, 94(3), 603–613.
   Web of Science ®Google Scholar
• Li, B., Chun, H., and Zhao, H. (2012), ‘Sparse Estimation of Conditional Graphical Models with Application to Gene Networks’, Journal of the American Statistical Association, 107(497), 152–167.
   PubMed Web of Science ®Google Scholar
• Li, B., and Wang, S. (2007), ‘On Directional Regression for Dimension Reduction’, Journal of the American Statistical Association, 102(479), 997–1008.
   Web of Science ®Google Scholar
• Lin, Q., Zhao, Z., and Liu, J.S. (2018), ‘On Consistency and Sparsity for Sliced Inverse Regression in High Dimensions’, The Annals of Statistics, 46(2), 580–610.
   Web of Science ®Google Scholar
• Lin, Q., Zhao, Z., and Liu, J.S. (2019), ‘Sparse Sliced Inverse Regression Via Lasso’, Journal of the American Statistical Association, 114(528), 1726–1739.
   PubMed Web of Science ®Google Scholar
• Liu, B., Zhang, Q., Xue, L., Song, P.X.-K., and Kang, J. (2024), ‘Robust High-dimensional Regression with Coefficient Thresholding and Its Application to Imaging Data Analysis’, Journal of the American Statistical Association, 119, 715–729.
   PubMed Web of Science ®Google Scholar
• Luo, W., Xue, L., Yao, J., and Yu, X. (2022), ‘Inverse Moment Methods for Sufficient Forecasting Using High-dimensional Predictors’, Biometrika, 109(2), 473–487.
   Web of Science ®Google Scholar
• Ma, S. (2013), ‘Alternating Direction Method of Multipliers for Sparse Principal Component Analysis’, Journal of the Operations Research Society of China, 1(2), 253–274.
   Google Scholar
• Mackey, L.W. (2009), ‘Deflation Methods for Sparse PCA’, in Advances in Neural Information Processing Systems, pp. 1017–1024.
   Google Scholar
• Morgan, X.C., Kabakchiev, B., Waldron, L., Tyler, A.D., Tickle, T.L., Milgrom, R., Stempak, J.M., Gevers, D., Xavier, R.J., and Silverberg, M.S. (2015), ‘Associations Between Host Gene Expression, the Mucosal Microbiome, and Clinical Outcome in the Pelvic Pouch of Patients with Inflammatory Bowel Disease’, Genome Biology, 16(1), 67.
   PubMedGoogle Scholar
• Neykov, M., Lin, Q., and Liu, J.S. (2016), ‘Signed Support Recovery for Single Index Models in High-dimensions’, Annals of Mathematical Sciences and Applications, 1(2), 379–426.
   Web of Science ®Google Scholar
• Shi, L., Huang, X., Feng, Y., and Suykens, J. (2019), ‘Sparse Kernel Regression with Coefficient-based Lq-regularization’, Journal of Machine Learning Research, 20(116), 1–44.
   Google Scholar
• Stokkers, P., Van Aken, B., Basoski, N., Reitsma, P., Tytgat, G., and Van Deventer, S. (1998), ‘Five Genetic Markers in the Interleukin 1 Family in Relation to Inflammatory Bowel Disease’, Gut, 43(1), 33–39.
   PubMed Web of Science ®Google Scholar
• Tan, K., Shi, L., and Yu, Z. (2020), ‘Sparse SIR: Optimal Rates and Adaptive Estimation’, The Annals of Statistics, 48(1), 64–85. https://doi.org/10.1214/18-AOS1791.
   Web of Science ®Google Scholar
• Tan, K.M., Wang, Z., Zhang, T., Liu, H., and Cook, R.D. (2018), ‘A Convex Formulation for High-dimensional Sparse Sliced Inverse Regression’, Biometrika, 105(4), 769–782.
   Web of Science ®Google Scholar
• Wold, S., Esbensen, K., and Geladi, P. (1987), ‘Principal Component Analysis’, Chemometrics and Intelligent Laboratory Systems, 2(1-3), 37–52.
   Web of Science ®Google Scholar
• Wu, C., Miller, J., Chang, Y., Sznaier, M., and Dy, J. (2019), ‘Solving Interpretable Kernel Dimensionality Reduction’, in Advances in Neural Information Processing Systems, pp. 7915–7925.
   Google Scholar
• Ying, C., and Yu, Z. (2022), ‘Fréchet Sufficient Dimension Reduction for Random Objects’, Biometrika, 109(4), 975–992.
   Web of Science ®Google Scholar
• Yu, X., Yao, J., and Xue, L. (2022), ‘Nonparametric Estimation and Conformal Inference of the Sufficient Forecasting with a Diverging Number of Factors’, Journal of Business & Economic Statistics, 40(1), 342–354.
   Web of Science ®Google Scholar
• Zhang, C.-H. (2010), ‘Nearly Unbiased Variable Selection Under Minimax Concave Penalty’, The Annals of Statistics, 38(2), 894–942.
   Web of Science ®Google Scholar
• Zhang, Q., Li, B., and Xue, L. (2024), ‘Nonlinear Sufficient Dimension Reduction for Distribution-on-distribution Regression’, Journal of Multivariate Analysis, 202, 105302.
   PubMed Web of Science ®Google Scholar
• Zhang, Q., Xue, L., and Li, B. (2024), ‘Dimension Reduction for Fréchet Regression’, Journal of the American Statistical Association, in press.
   Web of Science ®Google Scholar
• Zou, H. (2006), ‘The Adaptive Lasso and Its Oracle Properties’, Journal of the American Statistical Association, 101(476), 1418–1429.
   Web of Science ®Google Scholar
• Zou, H., Hastie, T., and Tibshirani, R. (2006), ‘Sparse Principal Component Analysis’, Journal of Computational and Graphical Statistics, 15(2), 265–286.
   Web of Science ®Google Scholar
• Zou, H., and Xue, L. (2018), ‘A Selective Overview of Sparse Principal Component Analysis’, Proceedings of the IEEE, 106(8), 1311–1320.
   Web of Science ®Google Scholar