ADAPTIVE LOW-NONNEGATIVE-RANK APPROXIMATION FOR STATE AGGREGATION OF MARKOV CHAINS

doi:10.1137/18M1220790

CSpace

	ADAPTIVE LOW-NONNEGATIVE-RANK APPROXIMATION FOR STATE AGGREGATION OF MARKOV CHAINS
	Duan, Yaqi 1; Wang, Mengdi 1; Wen, Zaiwen 2; Yuan, Yaxiang 3
	2020
发表期刊	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN	0895-4798
卷号	41 期号:1 页码:244-278
摘要	This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of metastates. The number of metastates is characterized by the nonnegative rank of the Markov transition matrix. Motivated by the success of the nuclear norm relaxation in low-rank minimization problems, we propose an atomic regularizer as a convex surrogate for the nonnegative rank and formulate a convex optimization problem. Because the atomic regularizer itself is not computationally tractable, we instead solve a sequence of problems involving a nonnegative factorization of the Markov transition matrices by using the proximal alternating linearized minimization method. Two methods for adjusting the rank of factorization are developed so that local minima are escaped. One is to append an additional column to the factorized matrices, which can be interpreted as an approximation of a negative subgradient step. The other is to reduce redundant dimensions by means of linear combinations. Overall, the proposed algorithm very likely converges to the global solution. The efficiency and statistical properties of our approach are illustrated on synthetic data. We also apply our state aggregation algorithm on a Manhattan transportation data set and make extensive comparisons with an existing method.
关键词	Markov chain state aggregation nonnegative matrix factorization atomic norm proximal alternating linearized minimization
DOI	10.1137/18M1220790
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11831002] ; National Natural Science Foundation of China[11421101] ; Beijing Academy of Artificial Intelligence (BAAI)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000546980200011
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51724
专题	中国科学院数学与系统科学研究院
通讯作者	Duan, Yaqi
作者单位	1.Princeton Univ, Dept Elect Engn, Princeton, NJ 08544 USA 2.Peking Univ, Natl Engn Lab Big Data Anal & Applicat, Beijing Int Ctr Math Res, Ctr Data Sci, Beijing, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Duan, Yaqi,Wang, Mengdi,Wen, Zaiwen,et al. ADAPTIVE LOW-NONNEGATIVE-RANK APPROXIMATION FOR STATE AGGREGATION OF MARKOV CHAINS[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2020,41(1):244-278.
APA	Duan, Yaqi,Wang, Mengdi,Wen, Zaiwen,&Yuan, Yaxiang.(2020).ADAPTIVE LOW-NONNEGATIVE-RANK APPROXIMATION FOR STATE AGGREGATION OF MARKOV CHAINS.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,41(1),244-278.
MLA	Duan, Yaqi,et al."ADAPTIVE LOW-NONNEGATIVE-RANK APPROXIMATION FOR STATE AGGREGATION OF MARKOV CHAINS".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 41.1(2020):244-278.