Weakly decomposable regularization penalties and structured sparsity

TL;DR

This paper investigates the properties of weakly decomposable regularization penalties, extending the understanding of oracle properties from the Lasso to more general norm-based penalties.

Contribution

It introduces the weak decomposability condition for penalties and analyzes its role in achieving oracle properties beyond the Lasso.

Findings

Weak decomposability enables sharp oracle results for a broad class of penalties.

Extension of oracle property analysis from Lasso to general norm-based penalties.

Identification of conditions under which structured sparsity can be effectively enforced.

Abstract

It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then extends the situation to general norm-based penalties that satisfy a weak decomposability condition.