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arXiv · 1307.5601

Kinetic Energy Plus Penalty Functions for Sparse Estimation

Zhihua Zhang·Shibo Zhao·Zebang Shen·Shuchang Zhou
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Abstract

In this paper we propose and study a family of sparsity-inducing penalty functions. Since the penalty functions are related to the kinetic energy in special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We construct the KEP function by using the concave conjugate of a $χ^2$-distance function and present several novel insights into the KEP function with $q=1$. In particular, we derive a thresholding operator based on the KEP function, and prove its mathematical properties and asymptotic properties in sparsity modeling. Moreover, we show that a coordinate descent algorithm is especially appropriate for the KEP function. Additionally, we discuss the relationship of KEP with the penalty functions $\ell_{1/2}$ and MCP. The theoretical and empirical analysis validates that the KEP function is effective and efficient in high-dimensional data modeling.

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Zhihua Zhang, Shibo Zhao, Zebang Shen, Shuchang Zhou. 2014-07-06. Kinetic Energy Plus Penalty Functions for Sparse Estimation. https://arxiv.org/abs/1307.5601

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