Sparse Sufficient Dimension Reduction for Markov Blanket Discovery

Abstract

In this article, we propose to use sparse sufficient dimension reduction as a novel method for Markov blanket discovery of a target variable, where we do not take any distributional assumption on the variables. By assuming sparsity on the basis of the central subspace, we developed a penalized loss function estimate on the high-dimensional covariance matrix. A coordinate descent algorithm based on an inverse regression is used to get the sparse basis of the central subspace. Finite sample behavior of the proposed method is explored by simulation study and real data examples.

Keywords:

• Markov blanket
• Structural learning
• Sufficient dimension reduction

Mathematics Subject Classification:

• 62H12
• 62J99