稀疏统计学习及其最新研究进展综述  

A Review of Sparse Statistical Learning and Its Recent Research Progress

作　　者：张红英[1] 董珂臻 ZHANG Hongying;DONG Kezhen(School of Mathematics and Statistics,Xi′an Jiaotong University,Xi′an 710049,China)

机构地区：[1]西安交通大学数学与统计学院,西安710049

出　　处：《西南师范大学学报（自然科学版）》2023年第4期1-12,共12页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(12171386,11671007)。

摘　　要：稀疏性意谓可以仅用少数位于低维子空间的参数(特征变量)近似表示高维空间的复杂物理过程,是实际应用中普遍存在的性质.稀疏统计学习旨在探索高维数据的稀疏性,并进行统计建模和推断.文章综述了基于回归分析的稀疏统计学习模型及其最新研究进展.主要介绍了各类带有凸或非凸正则项的稀疏回归模型,特别是L_(1/2)正则化框架的算法和应用.近10年来,深度学习取得革命性进展,结合传统稀疏统计学习模型与深度神经网络的研究逐渐受到了广泛的关注.文章主要介绍了基于稀疏建模的深度学习方法和数据驱动的稀疏统计分析方法,前者包括深度网络展开等,后者则包括深度哈希学习及深度典型相关分析.最后,文章进行了总结,并展望了未来可能的研究方向.Sparsity means that complex physical processes in high-dimensional spaces can be approximated by only a few parameters(characteristic variables)located in low-dimensional subspaces,and is a prevalent property in practical applications.Sparse statistical learning aims to explore the sparsity of high-dimensional data and to perform statistical modeling and inference.The article reviews the sparse statistical learning models with a focus on regression analysis and its recent research progress.It mainly introduces various types of sparse regression models with convex or non-convex regularization terms,especially the algorithms and applications of L_(1/2)-regularization framework.In the last decade,deep learning has made revolutionary progress,and the research combining traditional sparse statistical learning models with deep neural networks has gradually received widespread attention.The article mainly introduces the deep learning methods based on sparse modeling and data-driven sparse statistical analysis methods,the former including deep unfolding networks and so on,and the latter including deep hash learning and deep canonical correlation analysis.Finally,the article concludes with a summary and looks at possible future research directions.

关 键 词：稀疏性 正则化框架 正则项 L_(1/2)正则化框架 深度学习 深度网络展开 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]