Post-Selection Inference for Sparse Estimation

TL;DR

This paper reviews methods for conducting valid statistical inference after model selection in sparse estimation, focusing on techniques like Lasso, Forward Stepwise, and LARS, and discusses related significance and spacing tests.

Contribution

It provides a comprehensive review of post-selection inference methods for sparse estimation, including polyhedral and truncated distribution approaches.

Findings

Discusses selective inference for Lasso, Forward Stepwise, and LARS.

Explains polyhedra and truncated distributions in post-selection inference.

Reviews significance and spacing tests for model selection methods.

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.