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Robust Bayesian matrix decomposition with mixture of Gaussian noise

文献类型：期刊论文

作者Wang, Haohui3; Zhang, Chihao1,2; Zhang, Shihua1,2
刊名NEUROCOMPUTING
出版日期2021-08-18
卷号449页码:108-116
关键词Bayesian method Matrix decomposition Maximum a posterior Mixture of Gaussians
ISSN号0925-2312
DOI10.1016/j.neucom.2021.04.004
英文摘要Matrix decomposition is a popular and fundamental approach in machine learning. The classical matrix decomposition methods with Frobenius norm loss is only optimal for Gaussian noise and thus suffer from the sensitivity to outliers and non-Gaussian noise. To address these limitations, the proposed methods can be divided into two categories. One type of approach is to replace the Frobenius norm loss with robust loss functions. The other type of approach is to impose the Bayesian priors to reduce the risk of overfitting. This paper combines these two approaches. Specifically, we model the noise by a mixture of Gaussian distribution, enabling the model to approximate a wide range of noise distributions. Meanwhile, we put a Laplace prior on the basis matrix to enforce the sparsity and a Dirichlet prior on the coefficient matrix to improve the interpretability. Extensive experiments in synthetic data and real-world data demonstrate that this method outperforms several competing ones. Ablation studies show that this method benefits from both the Bayesian priors and the Mixture of Gaussian noise loss, which confirms the necessity of combining the two schemes. (c) 2021 Elsevier B.V. All rights reserved.
资助项目National Key Research and Development Program of China[2019YFA0709501] ; National Natural Science Foundation of China[11661141019] ; National Natural Science Foundation of China[61621003] ; National Ten Thousand Talent Program for Young Topnotch Talents ; CAS Frontier Science Research Key Project for Top Young Scientist[QYZDBSSWSYS008]
WOS研究方向Computer Science
语种英语
WOS记录号WOS:000652818400010
出版者ELSEVIER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58707]  
专题应用数学研究所
通讯作者Zhang, Shihua
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Chinese Acad Sci, NCMIS, CEMS, RCSDS,Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China
推荐引用方式
GB/T 7714		 Wang, Haohui,Zhang, Chihao,Zhang, Shihua. Robust Bayesian matrix decomposition with mixture of Gaussian noise[J]. NEUROCOMPUTING,2021,449:108-116.
APA Wang, Haohui,Zhang, Chihao,&Zhang, Shihua.(2021).Robust Bayesian matrix decomposition with mixture of Gaussian noise.NEUROCOMPUTING,449,108-116.
MLA Wang, Haohui,et al."Robust Bayesian matrix decomposition with mixture of Gaussian noise".NEUROCOMPUTING 449(2021):108-116.

入库方式： OAI收割

来源：数学与系统科学研究院

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