Joint Modeling for Mean Vector and Covariance Estimation with l1-Penalty
2
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
In this study, we develop a novel updating-based method for penalized estimators for the mean vector and the covariance matrix. With a linear combination of predictors, the coefficients can be estimated by maximizing a penalized log likelihood function, and using coordinate descent algorithm is used to handle the l1-penalized function. In order to estimate the inverse covariance matrix estimation, we adopt a modified Cholesky decomposition so that to guarantee the positive definiteness of the estimators. In the genomic data analysis setting, we show that the proposed method can be efficiently used to detect the conditional independence among a group of genes, while adjusting for shared genetic effects. Simulation experiments benchmark the performance of the proposed method against another existing method.
Abstract
In this study, we develop a novel updating-based method for penalized estimators for the mean vector and the covariance matrix. With a linear combination of predictors, the coefficients can be estimated by maximizing a penalized log likelihood function, and using coordinate descent algorithm is used to handle the l1-penalized function. In order to estimate the inverse covariance matrix estimation, we adopt a modified Cholesky decomposition so that to guarantee the positive definiteness of the estimators. In the genomic data analysis setting, we show that the proposed method can be efficiently used to detect the conditional independence among a group of genes, while adjusting for shared genetic effects. Simulation experiments benchmark the performance of the proposed method against another existing method.
참고문헌 (13)
- Yin J, "A sparse conditional gaussian graphical model for analysis of genetical genomics data", Ann Appl Stat, 5, pp.2630~2650 (2011)
- Li B, "Sparse estimation conditional graphical models with applications to gene network", J Am Stat Assoc, 107, pp.152~167 (2012)
- Cai T, "Covariate-adjusted precision matrix estimation with an application in genetical genomics", Biometrika, 100, pp.139~156 (2013)
- Chun H, "Joint conditional gaussian graphical models with multiple sources of genomic data", Front Genet, 4, pp.294~ (2013)
- Zhang L, "Learning gene networks under snp perturbations using eqtl datasets", PLOS Comput Biol, 10, pp.e1003420~ (2014)
- Pourahmadi M, "Joint mean-covariance models with applications to longitudinal data: unconstrained parameterization", Biometrika, 86, pp.677~690 (1999)
- Chang C, "Estimation of covariance matrix via the sparse cholesky factor with lasso", J Stat Plan Infer, 140, pp.3858~3873 (2010)
- Tibshirani R, "Regression shrinkage and selection via the lasso", J Roy Stat Soc B Met, 58, pp.267~288 (1996)
- Huang JZ, "Covariance matrix selection and estimation via penalized normal likelihood", Biometrika, 93, pp.85~98 (2006)
- Friedman J, "Regularization paths for generalized linear models via coordinate descent", J Stat Softw, 33, pp.1~22 (2010)
- Lee JJ, "Variable selection and joint estimation of mean and covariance models with an application to eQTL data", J Appl Stat (2016)
- Fan J, "Variable selection via nonconcave penalized likelihood and its oracle properties", J Am Stat Assoc, 96, pp.1348~1360 (2001)
- Zhang CH, "Nearly unbiased variable selection under minimax concave penalty", Ann Stat, 38, pp.894~942 (2010)