A General Framework of Dual Certificate Analysis for Structured Sparse Recovery Problems
This provides a foundational tool for researchers in machine learning and signal processing working on sparse recovery, though it is incremental in building upon prior dual certificate ideas.
The paper tackles the lack of a general theory for analyzing structured sparse recovery problems by introducing a unified framework based on dual certificates, which improves existing results for methods like L1 regularization.
This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work, due to the lack of a general and coherent theory, the analysis has so far only been carried out in limited scopes for specific problems. In this context the current paper makes two contributions. First, we introduce a general definition of dual certificate, which we then use to develop a unified theory of sparse recovery analysis for convex programming. Second, we present a class of structured sparsity regularization called structured Lasso for which calculations can be readily performed under our theoretical framework. This new theory includes many seemingly loosely related previous work as special cases; it also implies new results that improve existing ones even for standard formulations such as L1 regularization.