L₀-Regularized Learning for High-Dimensional Additive Hazards Regression

References

• Aalen O (1980) A Model for Nonparametric Regression Analysis of Counting Processes (Springer, New York).Crossref, Google Scholar
• Andersen P, Gill R (1982) Cox’s regression model for counting processes: A large sample study. Ann. Statist. 10(4):1100–1120.Crossref, Google Scholar
• Barron A, Birge L, Massart P (1999) Risk bounds for model selection via penalization. Probab. Theory Related Fields 113(3):301–413.Crossref, Google Scholar
• Belloni A, Chernozhukov V, Wang L (2011) Square-root Lasso: Pivotal recovery of sparse signals via conic programming. Biometrika 98(4):791–806.Crossref, Google Scholar
• Belloni A, Chernozhukov V, Fernandez-Val I, Hansen C (2017) Program evaluation and causal inference with high-dimensional data. Econometrica 85(1):233–298.Crossref, Google Scholar
• Bertsimas D, King A, Mazumder R (2016) Best subset selection via a modern optimization lens. Ann. Statist. 44(2):813–852.Crossref, Google Scholar
• Bickel P, Ritov Y, Tsybakov A (2009) Simultaneous analysis of Lasso and Dantzig selector. Ann. Statist. 37(4):1705–1732.Crossref, Google Scholar
• Breslow N, Day N (1987) Statistical Methods in Cancer Research, 2: The Design and Analysis of Case-Control Studies (IARC, Lyon, France).Google Scholar
• Bühlmann P, van de Geer S (2011) Statistics for High-Dimensional Data: Methods, Theory and Applications (Springer, Berlin).Crossref, Google Scholar
• Candès E, Tao T (2007) The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Statist. 35(6):2313–2351.Crossref, Google Scholar
• Candès E, Fan Y, Janson L, Lv J (2018) Panning for gold: ‘Model-X’ knockoffs for high dimensional controlled variable selection. J. Roy. Statist. Soc. Ser. B. Statist. Methodology 80(3):551–577.Crossref, Google Scholar
• Chen M, Ren Z, Zhao H, Zhou H (2016) Asymptotically normal and efficient estimation of covariate-adjusted Gaussian graphical model. J. Amer. Statist. Assoc. 111(513):394–406.Crossref, Google Scholar
• Cheng X, Zhang J, Yan L (2020) Understanding the impact of individual users’ rating characteristics on the predictive accuracy of recommender systems. INFORMS J. Comput. 32(2):303–320.Abstract, Google Scholar
• Cox D (1972) Regression models and life-tables. J. Roy. Statist. Soc. Ser. B. Statist. Methodology 34(2):187–220.Google Scholar
• Cox D, Oakes D (1980) Analysis of Survival Data (Chapman and Hall, London).Google Scholar
• Efron B, Hastie T, Johnstone I, Tibshirani R (2004) Least angle regression (with discussions). Ann. Statist. 32(2):407–499.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 J, Lv J (2010) A selective overview of variable selection in high dimensional feature space. Statist. Sinica 20(1):101–148.Google Scholar
• Fan J, Guo S, Hao N (2012) Variance estimation using refitted cross-validation in ultrahigh dimensional regression. J. Roy. Statist. Soc. Ser. B. Statist. Methodology 74(1):37–65.Crossref, Google Scholar
• Fan J, Lv J, Qi L (2011) Sparse high dimensional models in economics. Annual Rev. Econom. 3(1):291–317.Crossref, Google Scholar
• Fan Y, Lv J (2016) Innovated scalable efficient estimation in ultra-large Gaussian graphical models. Ann. Statist. 44(5):2098–2126.Crossref, Google Scholar
• Fan Y, Tang C (2013) Tuning parameter selection in high dimensional penalized likelihood. J. Roy. Statist. Soc. Ser. B. Statist. Methodology 75(3):531–552.Crossref, Google Scholar
• Faraggi D, Simon R (1995) A neural network model for survival data. Statist. Medicine 14(1):73–82.Crossref, Google Scholar
• Gorst-Rasmussen A, Scheike TH (2012) Coordinate descent methods for the penalized semiparametric additive hazards model. J. Statist. Software 47(9):1–17.Crossref, Google Scholar
• Harrell FE, Califf RM, Pryor DB, Lee KL, Rosati RA (1982) Evaluating the yield of medical tests. J. Amer. Medical Assoc. 247(18):2543–2546.Crossref, Google Scholar
• Hastie T, Tibshirani R, Friedman J (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed. (Springer, Berlin).Crossref, Google Scholar
• Huang J, Jiao Y, Liu Y, Lu X (2018) A constructive approach to l0 penalized regression. J. Machine Learning Res. 19(10):1–37.Google Scholar
• Ishwaran H, Kogalur UB, Blackstone EH, Lauer MS (2008) Random survival forest. Ann. Appl. Statist. 2:841–860.Crossref, Google Scholar
• Ishwaran H, Kogalur UB, Gorodeski EZ, Minn AJ, Lauer MS (2010) High-dimensional variable selection for survival data. J. Amer. Statist. Assoc. 105(489):205–217.Crossref, Google Scholar
• Jarrow R (2009) Credit risk models. Annual Rev. Financial Econom. 1(1):37–68.Crossref, Google Scholar
• Jiao Y, Jin B, Lu X (2015) A primal dual active set with continuation algorithm for the l0-regularized optimization problem. Appl. Comput. Harmonic Anal. 39(3):400–426.Crossref, Google Scholar
• Katzman JL, Shaham U, Cloninger A, Bates J, Kluger Y (2018) DeepSurv: Personalized treatment recommender system using a Cox proportional hazards deep neural network. BMC Medical Res. Methodology 18(1):1–12.Crossref, Google Scholar
• Lando D (1998) On Cox processes and credit risky securities. Rev. Derivatives Res. 2(2–3):99–120.Crossref, Google Scholar
• Lee C, Zame W, Yoon J, Van der Schaar M (2018) DeepHit: A deep learning approach to survival analysis with competing risks. Proc. 32th AAAI Conf. Artificial Intelligence 32(1):2314–2321.Google Scholar
• Leng C, Ma S (2007) Path consistent model selection in additive risk model via Lasso. Statist. Medicine 26(20):3753–3770.Crossref, Google Scholar
• Lin W, Lv J (2013) High-dimensional sparse additive hazards regression. J. Amer. Statist. Assoc. 108(501):247–264.Crossref, Google Scholar
• Lin D, Ying Z (1994) Semiparametric analysis of the additive risk model. Biometrika 81(1):61–71.Crossref, Google Scholar
• Lu X, Rudi A, Borgonovo E, Rosasco L (2020) Faster kriging: Facing high-dimensional simulators. Oper. Res. 68(1):233–249.Link, Google Scholar
• Luo S, Xu J, Chen Z (2015) Extended Bayesian information criterion in the Cox model with a high-dimensional feature space. Ann. Inst. Statist. Math. 67(2):287–311.Crossref, Google Scholar
• Lv J, Fan Y (2009) A unified approach to model selection and sparse recovery using regularized least squares. Ann. Statist. 37(6A):3498–3528.Crossref, Google Scholar
• Martinussen T, Scheike T (2009) Covariate selection for the semiparametric additive risk model. Scandinavian J. Statist. 36(4):602–619.Crossref, Google Scholar
• Mckeague I, Sasieni P (1994) A partly parametric additive risk model. Biometrika 81(3):501–514.Crossref, Google Scholar
• Paulson C, Luo L, James G (2018) Efficient large-scale internet media selection optimization for online display advertising. J. Marketing Res. 55(4):489–506.Crossref, Google Scholar
• Radchenko P, James G (2008) Variable inclusion and shrinkage algorithms. J. Amer. Statist. Assoc. 103(483):1304–1315.Crossref, Google Scholar
• Simon N, Friedman JH, Hastie T, Tibshirani R (2011) Regularization paths for Cox’s proportional hazards model via coordinate descent. J. Statist. Software 39(05):1–13.Crossref, Google Scholar
• Sørlie T, Tibshirani R, Parker J, Hastie T, Marron JS, Nobel A, Deng S, et al. (2003) Repeated observation of breast tumor subtypes in independent gene expression data sets. Proc. National Acad. Sci. USA 100(14):8418–8423.Crossref, Google Scholar
• Sun T, Zhang C (2012) Scaled sparse linear regression. Biometrika 99(4):879–898.Crossref, Google Scholar
• Tang C, Leng C (2010) Penalized high-dimensional empirical likelihood. Biometrika 97(4):905–920.Crossref, Google Scholar
• Tibshirani R (1996) Regression shrinkage and selection via the Lasso. J. Roy. Statist. Soc. Ser. B. Statist. Methodology 58(1):267–288.Crossref, Google Scholar
• Uno H, Cai T, Pencina M, D’Agostino R, Wei L (2011) On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Statist. Medicine 30(10):1105–1117.Crossref, Google Scholar
• Van’t Veer L, Dai H, Van de Vijver M, He Y, Hart A, Mao M, Peterse H, et al. (2002) Gene expression profiling predicts clinical outcome of breast cancer. Nature 415:530–536.Crossref, Google Scholar
• Wang X, Pakbin A, Mortazavi B, Zhao H, Lee D (2020) BoXHED: Boosted eXact Hazard Estimator with Dynamic covariates. Proc. Machine Learning Res. 119:9973–9982.Google Scholar
• Won D, Manzour H, Chaovalitwongse W (2020) Convex optimization for group feature selection in networked data. INFORMS J. Comput. 32(1):182–198.Link, Google Scholar
• Xu H, Caramanis C, Mannor S (2016) Statistical optimization in high dimensions. Oper. Res. 64(4):958–979.Link, Google Scholar
• Xu J, Li W, Ying Z (2020) Variable screening for survival data in the presence of heterogeneous censoring. Scandinavian J. Statist. 47(4):1171–1191.Crossref, Google Scholar
• Yoshimasa U, Shinya T (2019) High-dimensional macroeconomic forecasting and variable selection via penalized regression. Econom. J. 22(1):34–56.Crossref, Google Scholar
• Zhang C (2010) Nearly unbiased variable selection under minimax concave penalty. Ann. Statist. 38(2):894–942.Crossref, Google Scholar
• Zhang H, Sun L, Zhou Y, Huang J (2017) Oracle inequalities and selection consistency for weighted Lasso in high-dimensional additive hazards model. Statist. Sinica 27(4):1903–1920.Google Scholar
• Zhao P, Yu B (2006) On model selection consistency of Lasso. J. Machine Learning Res. 7(12):2541–2563.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, Lv J, Lin W (2021) Nonsparse learning with latent variables. Oper. Res. 69(1):346–359.Link, Google Scholar
• Zhu J, Wen C, Zhu J, Zhang H, Wang X (2020) A polynomial algorithm for best-subset selection problem. Proc. National Acad. Sci. USA 117(52):33117–33123.Crossref, Google Scholar
• Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J. Roy. Statist. Soc. Ser. B. Statist. Methodology 67(2):301–320.Crossref, Google Scholar
• Zou H, Li R (2008) One-step sparse estimates in nonconcave penalized likelihood models. Ann. Statist. 36(4):1509–1533.Google Scholar