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Weighted Mnet Penalty for Twice Differentiable Convex Losses on High Dimensions : 고차원 자료에서 두 번 미분 가능한 볼록 손실 함수에 대한 WMnet 벌점화 방법 연구
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 김용대 | - |
dc.contributor.author | 김주유 | - |
dc.date.accessioned | 2017-07-14T00:31:20Z | - |
dc.date.available | 2017-07-14T00:31:20Z | - |
dc.date.issued | 2014-08 | - |
dc.identifier.other | 000000021297 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121149 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 통계학과, 2014. 8. 김용대. | - |
dc.description.abstract | In many regression problems, covariates can be naturally correlated. Kim and Jeon [2014] proposed weighted Mnet penalty which is defined combination of weighted minimax concave penalty(MCP) and weighted ridge penalty. They
showed that the weighted Mnet penalty is useful to squared loss when the covariates of correlations are highly correlated. They also point out that the weighted l2 penalty is equivalent to the Laplacian penalty with certain weights and the weighted Mnet estimator has the oracle property to the squared loss under regular conditions. We extend the weighted Mnet estimator to twice differentiable convex losses. We showed that the weighted l2 penalty to twice differentiable convex losses also can be equivalent to the Laplacian penalty with certain weights and the weighted Mnet has an oracle property on high dimensional model in the sense that it is equal to the oracle ridge estimator with high probability. By simulations and real data analysis, we show that the weighted Mnet penalty is a useful to the other competitors including the elastic net, the Ment and the sparse Laplacian penalty. | - |
dc.description.tableofcontents | Abstract i
1 Introduction 1 1.1 Overview 1 1.2 Outline of the thesis 5 2 Literature Review : Variable Selection Methods on High Dimensions 7 2.1 Sparse regularization methods 10 2.2 Penalties for highly correlated covariates 19 2.3 The weighted Mnet penalty for the squared loss 23 3 Theorical Properties : Weighted Mnet Penalty for Twice Differentiable Convex Losses 27 3.1 Definition and estimator of the weighted Mnet 27 3.2 Compare to Laplacian penalty on twice differentiable losses 28 3.3 Oracle property 30 3.3.1 Oracle weighted ridge estimator 30 3.3.2 Oracle property 31 4 Optimization Algorithm 34 4.1 Optimization algorithms for sparse penalized methods 35 4.1.1 Least Angle Regression(LARS) algorithm 35 4.1.2 Coordinate descent algorithm 36 4.2 Concave Convex Procedure(CCCP) 40 4.3 Optimization algorithm for the weighted Mnet estimator 42 5 Numerical studies 46 5.1 Simulation studies 47 5.2 Real data analysis 51 6 Concluding remarks 56 Appendix 57 Proof of the Theorem 1 59 Proof of the Theorem 2 62 Abstract (in Korean) 72 | - |
dc.format | application/pdf | - |
dc.format.extent | 593813 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | weighted Mnet penalty | - |
dc.subject | twice differentiable losses | - |
dc.subject | generalized linear model | - |
dc.subject | oracle ridge | - |
dc.subject.ddc | 519 | - |
dc.title | Weighted Mnet Penalty for Twice Differentiable Convex Losses on High Dimensions | - |
dc.title.alternative | 고차원 자료에서 두 번 미분 가능한 볼록 손실 함수에 대한 WMnet 벌점화 방법 연구 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Kim, Jooyoo | - |
dc.description.degree | Doctor | - |
dc.citation.pages | vi, 73 | - |
dc.contributor.affiliation | 자연과학대학 통계학과 | - |
dc.date.awarded | 2014-08 | - |
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