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Nonconvex Penalization, Levy Processes and Concave Conjugates
Zhihua Zhang · Bojun Tu

Mon Dec 03 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor

In this paper we study sparsity-inducing nonconvex penalty functions using Levy processes. We define such a penalty as the Laplace exponent of a subordinator. Accordingly, we propose a novel approach for the construction of sparsity-inducing nonconvex penalties. Particularly, we show that the nonconvex logarithmic (LOG) and exponential (EXP) penalty functions are the Laplace exponents of Gamma and compound Poisson subordinators, respectively. Additionaly, we explore the concave conjugate of nonconvex penalties. We find that the LOG and EXP penalties are the concave conjugates of the negatives of Kullback-Leiber (KL) distance functions. Furthermore, the relationship between these two penalties is due to asymmetricity of the KL distance.

Author Information

Zhihua Zhang (Shanghai Jiao Tong University)
Bojun Tu (Zhejiang University)

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