Post-Selection Inference for Sparse Estimation

Abstract

When the model is not known and parameter testing or interval estimation is conducted after model selection, it is necessary to consider selective inference. This paper discusses this issue in the context of sparse estimation. Firstly, we describe selective inference related to Lasso as per \cite{lee}, and then present polyhedra and truncated distributions when applying it to methods such as Forward Stepwise and LARS. Lastly, we discuss the Significance Test for Lasso by \cite{significant} and the Spacing Test for LARS by \cite{ryan_exact}. This paper serves as a review article. Keywords: post-selective inference, polyhedron, LARS, lasso, forward stepwise, significance test, spacing test.