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Structured Sparsity Promoting Functions: Theory And Applications, Erin Tripp

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Motivated by the minimax concave penalty based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions and their Moreau envelopes. Properties of these functions are developed by leveraging their structure. In particular, we show that the behavior of the constructed function can be easily controlled by assumptions on the original convex function. We provide sparsity guarantees for the general family of functions via the proximity operator. Results related to the Fenchel Conjugate and Łojasiewicz exponent of these functions are also provided. We further study the behavior …