Alternative models for the modified form of ridge regularized linear model in discovering Markov boundary

Abstract

Abstract It has been proved that the modified form of ridge regularized linear model (MRRLM) can discover a subset of Markov boundary of the target variable under some constrained conditions. However, MRRLM cannot be applied to the data sets with collinear variables due to covariance matrix is employed. To develop a suitable alternative model for MRRLM, we study the relationships of discovery performance of Markov boundary among MRRLM, ridge regression linear model (RRLM), and LASSO combining with permutation test through empirical method. In addition, we also proposed a new NVRRLM to discover Markov boundary of the target variable. The experimental results show that: (1) On the binary data sets, MRRLM has a basically similar performance with LASSO and RRLM; (2) On the continuous data sets, MRRLM has a basically similar discovery performance with LASSO but has higher discovery performance than RRLM; (3) The new NVRRLM can replace MRRLM on the data sets with collinear variables. The above experimental results demonstrate NVRRLM can effectively deal with variable collinearity problems.