minhdg00/penalized-mle-with-reparameterization

implement BCD to find l1-penalized MLE with appropriate parametrization multivariate GLM

Research project supervised by Prof. Sunyoung Shin.

• Proposed a penalized Gaussian maximum likelihood estimation and variable selection method with appropriate reparameterization in multiple response regression model, and wrote code for this algorithm

Main idea of the algorithm:

Make effort to provide a efficient Lasso type estimator with parameterization tricks. The algorithm's purpose is to tackle with sparsity and large number of features.

File Instruction

• dmlsim.R  is the simulation script
• JointSol_rep.R is revised DML algorithm by Lee & Liu to fit our case
• UpdatePhi_rep.c is the script to update the new parameter Phi
• cv_dml.R is the script containing cross validation as well as dmlpath function ( fit model for a vector of lambdas)

Note

• To run R code, you first need to compile the C code on your local machine
• With large size of data, the code can run very slow.

Reference

Städler, Nicolas & Bühlmann, Peter & van de Geer, Sara. (2010). L1-Penalization for Mixture Regression Models. TEST: An Official Journal of the Spanish Society of Statistics and Operations Research. 19. 209-256. 10.1007/s11749-010-0197-z.

Lee, Wonyul & Liu, Yufeng. (2012). Simultaneous Multiple Response Regression and Inverse Covariance Matrix Estimation via Penalized Gaussian Maximum Likelihood. Journal of multivariate analysis. 111. 241-255. 10.1016/j.jmva.2012.03.013.