Kinetic Energy Plus Penalty Functions for Sparse Estimation
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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 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 ℓ_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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