Fast Association Recovery in High Dimensions by Parallel Learning

References

• Abdi H (2007) Singular value decomposition (SVD) and generalized singular value decomposition. Encyclopedia of Measurement and Statistics 907(912):44.Google Scholar
• Bertsimas D, Parys BV (2020) Sparse high-dimensional regression. Ann. Statist. 48(1):300–323.Crossref, Google Scholar
• Bickel PJ, Ritov Y, Tsybakov AB (2009) Simultaneous analysis of lasso and Dantzig selector. Ann. Statist. 37(4):1705–1732.Crossref, Google Scholar
• Blumensath T, Davies ME (2009) Iterative hard thresholding for compressed sensing. Appl. Comput. Harmonic Anal. (Oxford) 27(3):265–274.Crossref, Google Scholar
• Brem RB, Kruglyak L (2005) The landscape of genetic complexity across 5,700 gene expression traits in yeast. Proc. Natl. Acad. Sci. USA 102(5):1572–1577.Crossref, Google Scholar
• Bunea F, She Y, Wegkamp MH (2011) Optimal selection of reduced rank estimators of high-dimensional matrices. Ann. Statist. 39(2):1282–1309.Crossref, Google Scholar
• Busygin S, Prokopyev O, Pardalos PM (2008) Biclustering in data mining. Comput. Oper. Res. 35(9):2964–2987.Crossref, Google Scholar
• Chen L, Huang JZ (2012) Sparse reduced-rank regression for simultaneous dimension reduction and variable selection. J. Amer. Statist. Assoc. 107(500):1533–1545.Crossref, Google Scholar
• Chen K, Wang W (2022) rrpack: Reduced-Rank Regression. R package version 0.1-13. https://CRAN.R-project.org/package=rrpack.Google Scholar
• Chen K, Chan KS, Stenseth NC (2012) Reduced rank stochastic regression with a sparse singular value decomposition. J. Roy. Statist. Soc. Ser. B (Statist. Methodology) 74(2):203–221.Crossref, Google Scholar
• Chen K, Dong H, Chan KS (2013) Reduced rank regression via adaptive nuclear norm penalization. Biometrika 100(4):901–920.Crossref, Google Scholar
• Chen K, Dong R, Xu W, Zheng Z (2022) Fast stagewise sparse factor regression. J. Machine Learn. Res. 23(271):1–45.Google Scholar
• Chen K, Hoffman EA, Seetharaman I, Jiao F, Lin CL, Chan KS (2016) Linking lung airway structure to pulmonary function via composite bridge regression. Ann. Appl. Statist. 10(4):1880.Crossref, Google Scholar
• Costa M, Gardini A, Paruolo P (1997) A reduced rank regression approach to tests of asset pricing. Oxford Bull. Econom. Statist. 59(1):163–181.Crossref, Google Scholar
• Cubadda G, Hecq A (2021) Reduced rank regression models in economics and finance. Working paper, University of Rome Tor Vergata, Roma.Google Scholar
• Demirkaya E, Feng Y, Basu P, Lv J (2022) Large-scale model selection in misspecified generalized linear models. Biometrika 109(1):123–136.Crossref, Google Scholar
• Dong R, Wen C (2025) Fast association recovery in high dimensions by parallel learning. https://doi.org/10.1287/ijoc.2024.0691.cd, https://github.com/INFORMSJoC/2024.0691.Google Scholar
• Dong R, Li D, Zheng Z (2021) Parallel integrative learning for large-scale multi-response regression with incomplete outcomes. Comput. Statist. Data Anal. (Oxford) 160:107243.Crossref, Google Scholar
• Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96(456):1348–1360.Crossref, Google Scholar
• Fan Y, Lv J (2014) Asymptotic properties for combined l 1 and concave regularization. Biometrika 101(1):57–70.Crossref, Google Scholar
• Fan Y, Tang CY (2013) Tuning parameter selection in high dimensional penalized likelihood. J. Roy. Statist. Soc. Ser. B (Statist. Methodology) 75(3):531–552.Crossref, Google Scholar
• Friedman J, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J. Statist. Software 33(1):1.Crossref, Google Scholar
• Ge R, Jin C, Zheng Y (2017) No spurious local minima in nonconvex low rank problems: A unified geometric analysis. Precup D, ed. Proc. Internat. Conf. Machine Learn. (JMLR.org), 1233–1242.Google Scholar
• Ge R, Lee JD, Ma T (2016) Matrix completion has no spurious local minimum. Lee DD, Sugiyama M, von Luxburg U, Guyon I, Garnett R, eds. Adv. Neural Inform. Processing Systems, vol. 29 (Curran Associates Inc., Red Hook, NY).Google Scholar
• Gustin MC, Albertyn J, Alexander M, Davenport K (1998) Map kinase pathways in the yeast Saccharomyces cerevisiae. Microbiology Molecular Biology Rev. 62(4):1264–1300.Crossref, Google Scholar
• Kallus N, Udell M (2020) Dynamic assortment personalization in high dimensions. Oper. Res. 68(4):1020–1037.Link, Google Scholar
• Kanehisa M, Goto S, Furumichi M, Tanabe M, Hirakawa M (2009) KEGG for representation and analysis of molecular networks involving diseases and drugs. Nucleic Acids Res. 38(suppl 1):D355–D360.Crossref, Google Scholar
• Lange K (2013) Chapter 8. Optimization, vol. 95 (Springer Science & Business Media, Berlin), 185–219.Crossref, Google Scholar
• Lee M, Shen H, Huang JZ, Marron JS (2010) Biclustering via sparse singular value decomposition. Biometrics 66(4):1087–1095.Crossref, Google Scholar
• Ma Z, Ma Z, Sun T (2020) Adaptive estimation in two-way sparse reduced-rank regression. Statist. Sinica 30(4):2179–2201.Google Scholar
• Ma X, Xiao L, Wong WH (2014) Learning regulatory programs by threshold SVD regression. Proc. Natl. Acad. Sci. USA 111(44):15675–15680.Crossref, Google Scholar
• Mazumder R, Radchenko P, Dedieu A (2023) Subset selection with shrinkage: Sparse linear modeling when the SNR is low. Oper. Res. 71(1):129–147.Google Scholar
• Mishra A, Chen K (2021) secure: Sequential Co-Sparse Factor Regression. R package version 0.6. https://cran.r-project.org/src/contrib/Archive/secure/secure_0.6.tar.gz.Google Scholar
• Mishra A, Dey DK, Chen K (2017) Sequential co-sparse factor regression. J. Comput. Graphical Statist. 26(4):814–825.Crossref, Google Scholar
• Moreira Costa C, Kreber D, Schmidt M (2022) An alternating method for cardinality-constrained optimization: A computational study for the best subset selection and sparse portfolio problems. INFORMS J. Comput. 34(6):2968–2988.Link, Google Scholar
• Nassar H, Veldt N, Mohammadi S, Grama A, Gleich DF (2018) Low rank spectral network alignment. Proc. World Wide Web Conf. (International World Wide Web Conferences Steering Committee, Republic and Canton of Geneva, CHE), 619–628.Google Scholar
• Reinsel GC, Velu RP, Chen K (2022) Multivariate Reduced-Rank Regression: Theory, Methods and Applications, vol. 225 (Springer Nature, New York).Crossref, Google Scholar
• Storey JD, Akey JM, Kruglyak L (2005) Multiple locus linkage analysis of genomewide expression in yeast. PLoS Biol. 3(8):e267.Crossref, Google Scholar
• Sun R, Luo ZQ (2016) Guaranteed matrix completion via non-convex factorization. IEEE Trans. Inform. Theory 62(11):6535–6579.Crossref, Google Scholar
• Sun T, Zhang CH (2012) Scaled sparse linear regression. Biometrika 99(4):879–898.Crossref, Google Scholar
• Tibshirani R (1996) Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B (Methodological) 58(1):267–288.Crossref, Google Scholar
• Uematsu Y, Tanaka S (2019) High-dimensional macroeconomic forecasting and variable selection via penalized regression. Econom. J. 22(1):34–56.Crossref, Google Scholar
• Uematsu Y, Fan Y, Chen K, Lv J, Lin W (2019) SOFAR: Large-scale association network learning. IEEE Trans. Inform. Theory 65(8):4924–4939.Crossref, Google Scholar
• Wen C, Zhang A, Quan S, Wang X (2020) Bess: An r package for best subset selection in linear, logistic and cox proportional hazards models. J. Statist. Software 94:1–24.Crossref, Google Scholar
• Wu CY, Ding JJ (2018) Occluded face recognition using low-rank regression with generalized gradient direction. Pattern Recognition 80:256–268.Crossref, Google Scholar
• Ye F, Zhang CH (2010) Rate minimaxity of the lasso and Dantzig selector for the LQ loss in LR balls. J. Machine Learn. Res. 11:3519–3540.Google Scholar
• Yu Y, Wang T, Samworth RJ (2015) A useful variant of the Davis–Kahan theorem for statisticians. Biometrika 102(2):315–323.Crossref, Google Scholar
• Yuan XT, Li P, Zhang T (2018) Gradient hard thresholding pursuit. J. Machine Learn. Res. 18(166):1–43.Google Scholar
• Yuan M, Ekici A, Lu Z, Monteiro R (2007) Dimension reduction and coefficient estimation in multivariate linear regression. J. Roy. Statist. Soc. Ser. B (Statist. Methodology) 69(3):329–346.Crossref, Google Scholar
• Zheng Z, Fan Y, Lv J (2014) High dimensional thresholded regression and shrinkage effect. J. Roy. Statist. Soc. Ser. B (Statist. Methodology) 76(3):627–649.Crossref, Google Scholar
• Zheng Z, Bahadori MT, Liu Y, Lv J (2019) Scalable interpretable multi-response regression via seed. J. Machine Learn. Res. 20(107):1–34.Google Scholar
• Zhu J, Wen C, Zhu J, Zhang H, Wang X (2020) A polynomial algorithm for best-subset selection problem. Proc. Natl. Acad. Sci. USA 117(52):33117–33123.Crossref, Google Scholar