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bi-level variable selection in semiparametric transformation models with right-censored data

COMPUTATIONAL STATISTICS 2021年第3期36卷 1661-1692页

作者： Zhong, Wenyan Lu, Xuewen Wu, Jingjing Univ Calgary Dept Math & Stat Calgary AB T2N 1N4 Canada MSD China Dept Biostat & Res Decis Sci Shanghai 200233 Peoples R China

In this article, we investigate bi-level variable selection approaches in semiparametric transformation models when a grouping structure of covariates is available. This large class of transformation models includes the Cox proportional hazards model and proportional odds model as special cases. For this class of models, there are only a few works on variable selection and all the selection methods are at individual variable level. To fill the gap of variable selection at both group and individual levels, we propose a penalized nonparametric maximum likelihood estimation method with three different penalties, i.e., group bridge (GB), adaptive group bridge (AGB) and composite group bridge (CGB), and develop their respective computational algorithms. Further, we prove that the resulting estimators from AGB and CGB have desirable oracle properties. Our simulation studies demonstrate that all the three penalties work well in bi-level variable selection, while AGB and CGB outperform GB when within-group sparsity is present. The proposed methods are applied to two real datasets for illustration.

关键词： bi-level variable selection Group bridge penalty Penalized regression Semiparametric transformation model

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A high-dimensional M-estimator framework for bi-level variable selection

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2022年第3期74卷 559-579页

作者： Luo, bin Gao, Xiaoli Duke Univ Dept Biostat & Bioinformat 2424 Erwin Rd Durham NC 27705 USA Univ North Carolina Greensboro Dept Math & Stat 116 Petty Bldg Greensboro NC 27402 USA

In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to encourage the bi-level variable selection consistently. bi-level variable selection has become even more challenging when data have heavy-tailed distribution or outliers exist in random errors and covariates. In this paper, we study a framework of high-dimensional M-estimation for bi-level variable selection. This framework encourages bi-level sparsity through a computationally efficient two-stage procedure. In theory, we provide sufficient conditions under which our two-stage penalized M-estimator possesses simultaneous local estimation consistency and the bi-level variable selection consistency if certain non-convex penalty functions are used at the group level. Both our simulation studies and real data analysis demonstrate satisfactory finite sample performance of the proposed estimators under different irregular settings.

关键词： bi-level variable selection Estimation consistency High dimensionality M-estimation Non-convexity

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Bayesian group bridge for bi-level variable selection

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2017年 110卷 115-133页

作者： Mallick, Himel Yi, Nengjun Harvard TH Chan Sch Publ Hlth Dept Biostat 655 Huntington Ave Boston MA 02115 USA Broad Inst & Harvard Program Med & Populat Genet Cambridge MA 02142 USA Univ Alabama Birmingham Sch Publ Hlth Dept Biostat Sect Stat Genet 1665 Univ Blvd Birmingham AL 35294 USA

A Bayesian bi-level variable selection method (BAGB: Bayesian Analysis of Group Bridge) is developed for regularized regression and classification. This new development is motivated by grouped data, where generic variables can be divided into multiple groups, with variables in the same group being mechanistically related or statistically correlated. As an alternative to frequentist group variable selection methods, BAGS incorporates structural information among predictors through a group-wise shrinkage prior. Posterior computation proceeds via an efficient MCMC algorithm. In addition to the usual ease of-interpretation of hierarchical linear models, the Bayesian formulation produces valid standard errors, a feature that is notably absent in the frequentist framework. Empirical evidence of the attractiveness of the method is illustrated by extensive Monte Carlo simulations and real data analysis. Finally, several extensions of this new approach are presented, providing a unified framework for bi-level variable selection in general models with flexible penalties. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Bayesian regularization Bayesian variable selection bi-level variable selection Group bridge Group variable selection MCMC

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DCA based approaches for bi-level variable selection and application for estimate multiple sparse covariance matrices

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NEUROCOMPUTING 2021年 466卷 162-177页

作者： Le Thi, Hoai An Phan, Duy Nhat Dinh, Tao Pham Univ Lorraine Dept IA LGIPM F-57000 Metz France Inst Univ France IUF Paris France Univ Normandie Lab Math INSA Rouen Caen France

variable selection plays an important role in analyzing high dimensional data and is a fundamental problem in machine learning. When the data possesses certain group structures in which individual variables are also meaningful scientifically, we are naturally interested in selecting important groups as well as important variables within the selected groups. This is referred to as the bi-level variable selection which is much more complex than the selection of individual variables. In recent years, research on the topic of variable selection is very active, but the majority of the work is focused on the individual variable selection. There is therefore a need to further develop more effective approaches for bi-level variable selection. Since DC (Difference of Convex functions) programming and DCA (DC Algorithm), powerful tools in non-convex programming framework, have been successfully investigated for individual variable selection, we believe that they could be efficiently exploited for the more difficult bi-level variable selection task. In that direction, we investigate in this work DC approximations of the mixed zero norm (l(0,0)) and the combined norm (l(0) + l(q,0)). The resulting approximate problems are then formulated as DC programs for which DCA based algorithms are introduced. As an application, these DCA schemes are developed for estimating multiple sparse covariance matrices sharing some common structures such as the locations or weights of non-zero elements. The experimental results on both simulated and real datasets indicate the efficiency of our algorithms. (C) 2021 Elsevier B.V. All rights reserved.

关键词： bi-level variable selection Mixed norm Nonconvex approximation Multiple covariance matrices DC programming DCA

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bi-level variable selection in semiparametric transformation mixture cure models for right-censored data

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第7期52卷 3006-3025页

作者： Wu, Jingjing Lu, Xuewen Zhong, Wenyan Univ Calgary Dept Math & Stat Calgary AB T2N 1N4 Canada MSD China Dept Biostat & Res Decis Sci Shanghai Peoples R China

We investigate the bi-level variable selection problem in semiparametric transformation mixture cure models (STMCM). In this type of mixture cure models, we consider a class of semiparametric transformation models for the conditional survival function and a logistic regression for the incidence component, then conduct group variable selection. The group bridge penalty is adopted for bi-level variable selection on both parts of the mixture cure models. Through simulation studies and real data analyses, we show that the proposed method can identify the important variables and groups that contribute to the cure proportion and the survival function for the uncured subjects, respectively.

关键词： bi-level variable selection Group bridge Mixture cure model Penalized regression Semiparametric transformation model

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Consistent bi-level variable selection via composite group bridge penalized regression

Consistent bi-level variable selection via composite group b...

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作者： Seetharaman, Indu Kansas State University

学位级别：master

We study the composite group bridge penalized regression methods for conducting bilevel variable selection in high dimensional linear regression models with a diverging number of predictors. The proposed method combines the ideas of bridge regression (Huang et al., 2008a) and group bridge regression (Huang et al., 2009), to achieve variable selection consistencyin both individual and group levels simultaneously, i.e., the important groups andthe important individual variables within each group can both be correctly identi ed withprobability approaching to one as the sample size increases to in nity. The method takes full advantage of the prior grouping information, and the established bi-level oracle properties ensure that the method is immune to possible group misidenti cation. A related adaptive group bridge estimator, which uses adaptive penalization for improving bi-level selection, is also investigated. Simulation studies show that the proposed methods have superior performance in comparison to many existing methods

关键词： bi-level variable selection High-dimensional data Oracle property Penalized regression Sparse models

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Optimal treatment regimes for competing risk data using doubly robust outcome weighted learning with bi-level variable selection

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2021年 158卷 107167页

作者： He, Yizeng Kim, Soyoung Kim, Mi-Ok Saber, Wael Ahn, Kwang Woo Med Coll Wisconsin Div Biostat Milwaukee WI 53226 USA Univ Calif San Francisco Dept Epidemiol & Biostat San Francisco CA 94143 USA Med Coll Wisconsin Div Hematol & Oncol Milwaukee WI 53226 USA

The goal of the optimal treatment regime is maximizing treatment benefits via personalized treatment assignments based on the observed patient and treatment characteristics. Parametric regression-based outcome learning approaches require exploring complex interplay between the outcome and treatment assignments adjusting for the patient and treatment covariates, yet correctly specifying such relationships is challenging. Thus, a robust method against misspecified models is desirable in practice. Parsimonious models are also desired to pursue a concise interpretation and to avoid including spurious predictors of the outcome or treatment benefits. These issues have not been comprehensively addressed in the presence of competing risks. Recognizing that competing risks and group variables are frequently present, we propose a doubly robust estimation with adaptive L-1 penalties to select important variables at both group and within-group levels for competing risks data. The proposed method is applied to hematopoietic cell transplantation data to personalize the graft source choice for treatment-related mortality (TRM). While the existing medical literature attempts to find a uniform solution ignoring the heterogeneity of the graft source effects on TRM, the analysis results show the effect of the graft source on TRM could be different depending on the patient-specific characteristics. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Competing risks bi-level variable selection Personalized medicine Optimal treatment regime

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Group regularization for zero-inflated negative binomial regression models with an application to health care demand in Germany

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STATISTICS IN MEDICINE 2018年第20期37卷 3012-3026页

作者： Chatterjee, Saptarshi Chowdhury, Shrabanti Mallick, Himel Banerjee, Prithish Garai, Broti Northern Illinois Univ Div Stat Dept Math Sci De Kalb IL 60115 USA Wayne State Univ Ctr Mol Med & Genet Sch Med Detroit MI 48202 USA Harvard TH Chan Sch Publ Hlth Dept Biostat Boston MA 02115 USA Broad Inst MIT & Harvard Program Med & Populat Genet Cambridge MA 02142 USA JP Morgan Chase & Co New York NY 10004 USA Monsanto Co Chesterfield MO 63017 USA Icahn Sch Med Mt Sinai Dept Genet & Genom Sci New York NY 10029 USA IQVIA Plymouth Meeting PA 19462 USA

In many biomedical applications, covariates are naturally grouped, with variables in the same group being systematically related or statistically correlated. Under such settings, variable selection must be conducted at both group and individual variable levels. Motivated by the widespread availability of zero-inflated count outcomes and grouped covariates in many practical applications, we consider group regularization for zero-inflated negative binomial regression models. Using a least squares approximation of the mixture likelihood and a variety of group-wise penalties on the coefficients, we propose a unified algorithm (Gooogle: Group Regularization for Zero-inflated Count Regression Models) to efficiently compute the entire regularization path of the estimators. We investigate the finite sample performance of these methods through extensive simulation experiments and the analysis of a German health care demand dataset. Finally, we derive theoretical properties of these methods under reasonable assumptions, which further provides deeper insight into the asymptotic behavior of these approaches. The open source software implementation of this method is publicly available at: .

关键词： bi-level variable selection group bridge group LASSO group regularization health care demand zero-inflated negative binomial

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LINKING LUNG AIRWAY STRUCTURE TO PULMONARY FUNCTION VIA COMPOSITE BRIDGE REGRESSION

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ANNALS OF APPLIED STATISTICS 2016年第4期10卷 1880-1906页

作者： Chen, Kun Hoffman, Eric A. Seetharaman, Indu Jiao, Feiran Lin, Ching-Long Chan, Kung-Sik Univ Connecticut Dept Stat Storrs CT 06029 USA Univ Iowa Dept Radiol Iowa City IA 52242 USA Kansas State Univ Dept Stat Manhattan KS 66506 USA Univ Iowa Dept Stat & Actuarial Sci Iowa City IA 52242 USA Univ Iowa Dept Mech & Ind Engn Iowa City IA 52242 USA

The human lung airway is a complex inverted tree-like structure. Detailed airway measurements can be extracted from MDCT-scanned lung images, such as segmental wall thickness, airway diameter, parent-child branch angles, etc. The wealth of lung airway data provides a unique opportunity for advancing our understanding of the fundamental structure-function relationships within the lung. An important problem is to construct and identify important lung airway features in normal subjects and connect these to standardized pulmonary function test results such as FEV1%. Among other things, the problem is complicated by the fact that a particular airway feature may be an important (relevant) predictor only when it pertains to segments of certain generations. Thus, the key is an efficient, consistent method for simultaneously conducting group selection (lung airway feature types) and within-group variable selection (airway generations), i.e., bi-level selection. Here we streamline a comprehensive procedure to process the lung airway data via imputation, normalization, transformation and groupwise principal component analysis, and then adopt a new composite penalized regression approach for conducting bi-level feature selection. As a prototype of composite penalization, the proposed composite bridge regression method is shown to admit an efficient algorithm, enjoy bi-level oracle properties and outperform several existing methods. We analyze the MDCT lung image data from a cohort of 132 subjects with normal lung function. Our results show that lung function in terms of FEV1% is promoted by having a less dense and more homogeneous lung comprising an airway whose segments enjoy more heterogeneity in wall thicknesses, larger mean diameters, lumen areas and branch angles. These data hold the potential of defining more accurately the "normal" subject population with borderline atypical lung functions that are clearly influenced by many genetic and environmental factors.

关键词： bi-level variable selection composite penalization feature extraction lung airway data pulmonary function tests

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Credit scoring of micro and small entrepreneurial firms in China

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INTERNATIONAL ENTREPRENEURSHIP AND MANAGEMENT JOURNAL 2021年第1期17卷 29-43页

作者： Wang, Chengbin Fang, Kuangnan Zheng, Chenlu Xu, Hechao Li, Zewei Taizhou Coll Univ Zhejiang Taizhou Small Micro Finance Inst Taizhou Peoples R China Xiamen Univ Sch Econ Xiamen Peoples R China Xiamen Univ Sch Management Xiamen Peoples R China

It is difficult for micro and small entrepreneurial firms (MSEFs) to access external financing from formal financial institutions because financial institutions cannot obtain sufficient and reliable credit information about MSEFs. With the development of the internet and data collection technologies, more and more data can be accessed from different sources, and logistic regression model often suffers from bad performance. In this paper, we propose a credit scoring model using composite MCP logistic regression and firstly apply the proposed method to predict the probability of default of MSEFs in China. The proposed method can carry out parameter estimation and automatic bi-level selection of variables simultaneously with respect to the grouping structure of variables. Empirical results of MSEFs with complex grouping structure data have shown that the proposed method outperforms forward stepwise logistic regression, MCP logistic regression and group MCP logistic regression. In addition, we find that gross salary, tax paid, bank and injury insurance information of MSEFs are the most important factors to predict the probability of default.

关键词： Credit scoring Micro and small entrepreneurial firms (MSEFs) Composite MCP bi-level variable selection Logistic regression

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