结构化稀疏学习
Learning with Structured Sparsity
摘要：
本文研究了一种新的学习公式称为结构稀疏，这是一个自然的扩展标准稀疏概念在统计学习和压缩感知。通过允许特征集上的任意结构，这个概念推广了近年来流行的组稀疏性思想。一个一般的理论开发的学习与结构稀疏性，编码的复杂性与结构的概念的基础上。结果表明，如果目标信号的编码复杂度是小的，那么可以实现改进的性能，通过使用编码复杂度正则化方法，它推广了标准的稀疏正则化。此外，提出了一种结构化贪婪算法，有效地解决了结构化稀疏问题。在适当的条件下，贪婪算法近似地解决了编码复杂度优化问题。实验证明了结构稀疏性在实际应用中优于标准稀疏性。
英文摘要：
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature set, this concept generalizes the group sparsity idea that has become popular in recent years. A general theory is developed for learning with structured sparsity, based on the notion of coding complexity associated with the structure. It is shown that if the coding complexity of the target signal is small, then one can achieve improved performance by using coding complexity regularization methods, which generalize the standard sparse regularization. Moreover, a structured greedy algorithm is proposed to efficiently solve the structured sparsity problem. It is shown that the greedy algorithm approximately solves the coding complexity optimization problem under appropriate conditions. Experiments are included to demonstrate the advantage of structured sparsity over standard sparsity on some real applications.
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