The seamless-L0 （SELO） penalty is a smooth function on [0, ∞） that very closely resembles the L0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for var...The seamless-L0 （SELO） penalty is a smooth function on [0, ∞） that very closely resembles the L0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, we first generalize SELO to a class of penalties retaining good features of SELO, and then propose variable selection and estimation in linear models using the proposed generalized SELO （GSELO） penalized least squares （PLS） approach. We show that the GSELO-PLS procedure possesses the oracle property and consistently selects the true model under some regularity conditions in the presence of a diverging number of variables. The entire path of GSELO-PLS estimates can be efficiently computed through a smoothing quasi-Newton （SQN） method. A modified BIC coupled with a continuation strategy is developed to select the optimal tuning parameter. Simulation studies and analysis of a clinical data are carried out to evaluate the finite sample performance of the proposed method. In addition, numerical experiments involving simulation studies and analysis of a microarray data are also conducted for GSELO-PLS in the high-dimensional settings.展开更多
The seamless-L_0(SELO) penalty is a smooth function that very closely resembles the L_0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selecti...The seamless-L_0(SELO) penalty is a smooth function that very closely resembles the L_0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, the authors first generalize the SELO penalty to a class of penalties retaining good features of SELO, and then develop variable selection and parameter estimation in Cox models using the proposed generalized SELO(GSELO) penalized log partial likelihood(PPL) approach. The authors show that the GSELO-PPL procedure possesses the oracle property with a diverging number of predictors under certain mild, interpretable regularity conditions. The entire path of GSELO-PPL estimates can be efficiently computed through a smoothing quasi-Newton(SQN) with continuation algorithm. The authors propose a consistent modified BIC(MBIC) tuning parameter selector for GSELO-PPL, and show that under some regularity conditions, the GSELOPPL-MBIC procedure consistently identifies the true model. Simulation studies and real data analysis are conducted to evaluate the finite sample performance of the proposed method.展开更多
Robust image recovery methods have been attracted more and more attention in recent decades for its good property of tolerating system errors or measuring noise. In this paper, we propose a new robust method （ESL-SEL...Robust image recovery methods have been attracted more and more attention in recent decades for its good property of tolerating system errors or measuring noise. In this paper, we propose a new robust method （ESL-SELO） to recover nosing image, which combine exponential loss function and seamless-L0 （SELO） penalty function to guarantee both accuracy and robustness of the estimator. Theoretical result showed that our method has a local optimal solution and good asymptotic properties. Finally, we compare our method with other methods in simulation which shows better robustness and takes much less time.展开更多
基金Supported by the National Natural Science Foundation of China(11501578,11501579,11701571,41572315)the Fundamental Research Funds for the Central Universities(CUGW150809)
文摘The seamless-L0 （SELO） penalty is a smooth function on [0, ∞） that very closely resembles the L0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, we first generalize SELO to a class of penalties retaining good features of SELO, and then propose variable selection and estimation in linear models using the proposed generalized SELO （GSELO） penalized least squares （PLS） approach. We show that the GSELO-PLS procedure possesses the oracle property and consistently selects the true model under some regularity conditions in the presence of a diverging number of variables. The entire path of GSELO-PLS estimates can be efficiently computed through a smoothing quasi-Newton （SQN） method. A modified BIC coupled with a continuation strategy is developed to select the optimal tuning parameter. Simulation studies and analysis of a clinical data are carried out to evaluate the finite sample performance of the proposed method. In addition, numerical experiments involving simulation studies and analysis of a microarray data are also conducted for GSELO-PLS in the high-dimensional settings.
基金supported by the National Natural Science Foundation of China under Grant Nos.11801531,11501578,11501579,11701571,11871474 and 41572315the Fundamental Research Funds for the Central Universities under Grant No.CUGW150809
文摘The seamless-L_0(SELO) penalty is a smooth function that very closely resembles the L_0 penalty, which has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection. In this paper, the authors first generalize the SELO penalty to a class of penalties retaining good features of SELO, and then develop variable selection and parameter estimation in Cox models using the proposed generalized SELO(GSELO) penalized log partial likelihood(PPL) approach. The authors show that the GSELO-PPL procedure possesses the oracle property with a diverging number of predictors under certain mild, interpretable regularity conditions. The entire path of GSELO-PPL estimates can be efficiently computed through a smoothing quasi-Newton(SQN) with continuation algorithm. The authors propose a consistent modified BIC(MBIC) tuning parameter selector for GSELO-PPL, and show that under some regularity conditions, the GSELOPPL-MBIC procedure consistently identifies the true model. Simulation studies and real data analysis are conducted to evaluate the finite sample performance of the proposed method.
基金The third author was supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China,11XNK026
文摘Robust image recovery methods have been attracted more and more attention in recent decades for its good property of tolerating system errors or measuring noise. In this paper, we propose a new robust method （ESL-SELO） to recover nosing image, which combine exponential loss function and seamless-L0 （SELO） penalty function to guarantee both accuracy and robustness of the estimator. Theoretical result showed that our method has a local optimal solution and good asymptotic properties. Finally, we compare our method with other methods in simulation which shows better robustness and takes much less time.
