arXiv subjects

Zheng Pan

Publications and source records attributed to Zheng Pan.

21 records · Page 2Linked to original sources

arXiv2017

A Novel Distance Matric: Generalized Relative Entropy

Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We presented the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy is presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric.

cs.IT↗

arXiv2014

On the Conditions of Sparse Parameter Estimation via Log-Sum Penalty Regularization

For high-dimensional sparse parameter estimation problems, Log-Sum Penalty (LSP) regularization effectively reduces the sampling sizes in practice. However, it still lacks theoretical analysis to support the experience from previous empirical study. The analysis of this article shows that, like $\ell_0$-regularization, $O(s)$ sampling size is enough for proper LSP, where $s$ is the non-zero components of the true parameter. We also propose an efficient algorithm to solve LSP regularization problem. The solutions given by the proposed algorithm give consistent parameter estimations under less restrictive conditions than $\ell_1$-regularization.

cs.IT↗

arXiv2014

Relaxed Sparse Eigenvalue Conditions for Sparse Estimation via Non-convex Regularized Regression

Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regularized regression, our sparse eigenvalue based conditions are weaker than that of L1-regularization for parameter estimation and sparseness estimation. For the approximate global and approximate stationary (AGAS) solutions, almost the same conditions are also enough. We show that the desired AGAS solutions can be obtained by coordinate descent (CD) based methods. Finally, we perform some experiments to show the performance of CD methods on giving AGAS solutions and the degree of weakness of the estimation conditions required by the sharp concave regularizers.

cs.LG↗