高维约束矩阵回归问题

doi:10.15960/j.cnki.issn.1007-6093.2017.02.004

运筹学学报

高维约束矩阵回归问题

孔令臣^1,* 陈丙振¹修乃华¹ 戚厚铎²

1. 北京交通大学理学院, 北京 100044; 2. 南安普顿大学数学科学学院, 南安普顿, 海菲尔德 SO17 1BJ 英国

收稿日期:2017-03-24 出版日期:2017-06-15 发布日期:2017-06-15
通讯作者: 孔令臣 E-mail: konglchen@126.com
基金资助:
国家自然科学基金(Nos.11431002, 11671029)

High-dimensional constrained matrix regression problems

KONG Lingchen^1,* CHEN Bingzhen¹ XIU Naihua¹ QI Houduo²

1. School of Science, Beijing Jiaotong University, Beijing 100044, China 2. School of Mathematics, University of Southampton, Highfield SO17 1BJ, Southampton, UK

Received:2017-03-24 Online:2017-06-15 Published:2017-06-15

摘要/Abstract

摘要：

高维约束矩阵回归是指高维情况下带非凸约束的多响应多预测统计回归问题, 其数学模型是一个NP-难的矩阵优化, 它在机器学习与人工智能、医学影像疾病诊疗、基因表达分析、脑神经网络、风险管理等领域有广泛应用. 从高维约束矩阵回归的优化理论和算法两方面总结和评述这些新成果, 同时, 列出了相应的重要文献.

关键词: 矩阵回归, 非凸约束, 矩阵优化, 优化理论, 优化算法

Abstract:

High-dimensional constrained matrix regression refers to non-convex constrained statistical regression with the multivariate responses and multivariate predictors in the high-dimensional setting. Its mathematical model is a matrix optimization, which is generally NP-hard and has a wide range of applications in a lot of areas such as machine learning and artificial intelligence, medical imaging and diagnosis, gene expression analysis, neural networks, risk management. This paper briefly reviews the new results on optimization theory and algorithm of high-dimensional constrained matrix regression. Moreover, we list the corresponding important references.

Key words: matrix regression, non-convex constraint, matrix optimization, optimization theory, optimization algorithm

孔令臣, 陈丙振, 修乃华, 戚厚铎. 高维约束矩阵回归问题[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2017.02.004.

KONG Lingchen, CHEN Bingzhen, XIU Naihua, QI Houduo. High-dimensional constrained matrix regression problems[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2017.02.004.

参考文献

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高维约束矩阵回归问题

High-dimensional constrained matrix regression problems

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