Model Selection Consistency of Lasso for Empirical Data

TL;DR

This paper examines the robustness and consistency of the Lasso method for model selection in high-dimensional, complex empirical datasets with diverse noise distributions and sparsity levels, supported by theory and simulations.

Contribution

It provides theoretical guarantees and empirical evidence demonstrating Lasso's robustness in high-dimensional, diverse data scenarios, extending understanding of its model selection consistency.

Findings

Lasso is robust across various data characteristics.

Theoretical guarantees support empirical observations.

Simulations confirm Lasso's effectiveness in high-dimensional settings.

Abstract

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is fixed while dimensionality grows with $n$. We consider the model selection problem of lasso for this kind of data. We investigate both theoretical guarantees and simulations, and show that the lasso is robust for various kinds of data.