A fundamental limitation to the reduction of Markov chains via aggregation

被引：0

作者：

Kotsalis, Georgios ^{[1
]}

Shamma, Jeff S. ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Elect & Comp Engn, Atlanta, GA 30332 USA

来源：

2012 50TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON) | 2012年

关键词：

MODELS;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper highlights a limitation of state space aggregation based model reduction of Markov chains. It is shown that within the set of Markov chains of a given dimension that admit an exact low order representation, the set of Markov chains where this exact low order representation can be extracted by means of aggregation based model reduction is a nowhere dense set.

引用

页码：1449 / 1454

页数：6

共 11 条

[1] The realization problem for hidden Markov models
Anderson, BDO
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1999, 12 (01) : 80 - 120
[2] Billingsley P., 1995, Probability and Measure
[3] Deng K., 2010, P IEEE C DEC CONTR A
[4] Optimal Kullback-Leibler Aggregation via Spectral Theory of Markov Chains
Deng, Kun
Mehta, Prashant G.
Meyn, Sean P.
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (12) : 2787 - 2802
[5] Ho B., 1966, Regelungstechnik, V14, P545, DOI DOI 10.1524/AUTO.1966.14.112.545
[6] Kotsalis G, 2011, IEEE DECIS CONTR P, P6558, DOI 10.1109/CDC.2011.6161404
[7] Balanced Truncation for a Class of Stochastic Jump Linear Systems and Model Reduction for Hidden Markov Models
Kotsalis, Georgios
Megretski, Alexandre
Dahleh, Munther A.
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (11) : 2543 - 2557
[8] Munkres J, 2000, Topology, VSecond
[9] Picci G., 1978, Recent Developments in Variable Structure Systems, Economics and Biology, V162, P288
[10] The complete realization problem for hidden Markov models: a survey and some new results
Vidyasagar, M.
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2011, 23 (1-3) : 1 - 65

← 1 2 →