基于无标度先验的图模型结构学习  

Structure learning in graphical models incorporating the scale-free prior

作　　者：郭骁[1] 张海[1,2] 吴奖伦 

机构地区：[1]西北大学数学学院,西安710127 [2]中国科学院数学与系统科学院应用数学所,北京100190 [3]Department of Mathematics,College of Science,Swansea University,Swansea SA2 8PP,UK

出　　处：《中国科学：信息科学》2016年第7期870-882,共13页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:11171272,11571011)资助项目

摘　　要：本文研究在无标度先验下,图模型的结构学习问题.提出新的正则化模型,其惩罚项为Log型和Lq型惩罚函数的复合,该模型包含无标度先验.本文使用重赋权迭代算法求解该模型.实验表明,所提出的新模型有效、实用,其在参数估计和模型选择方面均有良好效果.In this paper, we consider the problem of structure learning in graphical models under the prior that the underlying networks are scale free. We propose a novel regularization model, which incorporates the scale-free prior, with a penalty that is a hybrid of the Log-type and Lq-type penalty functions. An iterative reweighted L1 algorithm is employed to solve the model. Numerical studies show that our method is both effective and practical and performs well in terms of parameter estimation and model selection.

关 键 词：稀疏 无标度 图模型 重赋权算法 正则化 

分 类 号：O157.5[理学—数学] TP181[理学—基础数学]