Introduction to the Special Issue on Sparsity and Regularization Methods

TL;DR

This paper introduces a special issue focused on sparsity and regularization methods, addressing the challenges of high-dimensional data where traditional statistical tools are insufficient.

Contribution

It highlights the need for new statistical methodologies and theories tailored for high-dimensional data analysis involving sparsity and regularization techniques.

Findings

Emphasizes the limitations of classical statistical inference in high-dimensional settings.

Calls for development of novel methods for high-dimensional data analysis.

Focuses on sparsity and regularization as key tools in modern statistical inference.

Abstract

Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many data sets encountered in modern applications have dimensionality significantly larger than the number of training data available, and for such problems the classical statistical tools become inadequate. In order to analyze high-dimensional data, new statistical methodology and the corresponding theory have to be developed.