A Unifying Framework of High-Dimensional Sparse Estimation with Difference-of-Convex (DC) Regularizations

Understand

Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse).

• Non-convex penalties in specific forms are well-studied in the literature for sparse estimation.
• A recent work \cite{ahn2016difference} has pointed out that nearly all existing non-convex penalties can be represented as difference-of-convex (DC) functions, which can be expressed as the difference of two convex functions, while itself may not be convex.
• There is a large existing literature on the optimization problems when their objectives and/or constraints involve DC functions.