# RegEM

RegEM: Regularized Expectation Maximization The modules implement the regularized EM algorithm described in T. Schneider, 2001: Analysis of incomplete climate data: Estimation of mean values and covariance matrices and imputation of missing values. Journal of Climate, 14, 853-871. The EM algorithm for Gaussian data is based on iterated linear regression analyses. In the regularized EM algorithm, a regularized estimation method replaces the conditional maximum likelihood estimation of regression parameters in the conventional EM algorithm for Gaussian data. The modules here provide truncated total least squares (with fixed truncation parameter) and ridge regression with generalized cross-validation as regularized estimation methods. The implementation of the regularized EM algorithm is modular, so that the modules that perform he regularized estimation of regression parameters (e.g., ridge regression and generalized cross-validation) can be exchanged for other regularization methods and other methods of determiningca regularization parameter. Per-Christian Hansen’s Regularization Tools contain Matlab modules implementing a collection of regularization methods that can be adapted to fit into the framework of the EM algorithm. The generalized cross-validation modules of the regularized EM algorithm are adapted from Hansen’s generalized cross-validation modules. In the Matlab implementation of the regularized EM algorithm, more emphasis was placed on the modularity of the program code than on computational efficiency. The regularized EM algorithm is currently being developed further under a project funded by the National Science Foundation’s Paleo Perspectives on Climate Change program

## References in zbMATH (referenced in 17 articles )

Showing results 1 to 17 of 17.
Sorted by year (citations)
1. Barboza, Luis A.; Emile-Geay, Julien; Li, Bo; He, Wan: Efficient reconstructions of Common Era climate via integrated nested Laplace approximations (2019)
2. Deng, Wan-Yu; Liu, Dan; Dong, Ying-Ying: Feature selection and classification for high-dimensional incomplete multimodal data (2018)
3. Fan, Fengfeng; Li, Zhanhuai; Chen, Qun; Chen, Lei: Relational data imputation with quality guarantee (2018)
4. Butucea, Cristina; Zgheib, Rania: Adaptive test for large covariance matrices in presence of missing observations (2017)
5. Ma, Xiaofei; Zhong, Qiuyan: Missing value imputation method for disaster decision-making using K nearest neighbor (2016)
6. Guillot, Dominique; Rajaratnam, Bala; Emile-Geay, Julien: Statistical paleoclimate reconstructions via Markov random fields (2015)
7. Chen, Lin S.; Prentice, Ross L.; Wang, Pei: A penalized EM algorithm incorporating missing data mechanism for Gaussian parameter estimation (2014)
8. Lounici, Karim: High-dimensional covariance matrix estimation with missing observations (2014)
9. Luengo, Julián; Sáez, José A.; Herrera, Francisco: Missing data imputation for fuzzy rule-based classification systems (2012) ioport
10. Zhou, Ligang; Lai, Kin Keung; Yen, Jerome: Empirical models based on features ranking techniques for corporate financial distress prediction (2012)
11. Zuccolotto, Paola: Principal component analysis with interval imputed missing values (2012)
12. McShane, Blakeley B.; Wyner, Abraham J.: A statistical analysis of multiple temperature proxies: are reconstructions of surface temperatures over the last 1000 years reliable? (2011)
13. Lee, Terry C. K.; Tsao, Min; Zwiers, Francis W.: State-space model for proxy-based millennial reconstruction (2010)
14. Polikar, Robi; DePasquale, Joseph; Mohammed, Hussein Syed; Brown, Gavin; Kuncheva, Ludmilla I.: Learn(^++).MF: A random subspace approach for the missing feature problem (2010)
15. Chang, Roy Kwang Yang; Loo, Chu Kiong; Rao, M. V. C.: Enhanced probabilistic neural network with data imputation capabilities for machine-fault classification (2009) ioport
16. López-Rubio, Ezequiel; Ortiz-de-Lazcano-Lobato, Juan Miguel: Automatic model selection by cross-validation for probabilistic PCA (2009) ioport
17. Fiori, Simone: Neural systems with numerically matched input-output statistic: isotonic bivariate statistical modeling (2007) ioport