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