Computing the nearest reversible Markov chain

Please always quote using this URN: urn:nbn:de:0297-zib-53292
  • Reversible Markov chains are the basis of many applications. However, computing transition probabilities by a finite sampling of a Markov chain can lead to truncation errors. Even if the original Markov chain is reversible, the approximated Markov chain might be non-reversible and will lose important properties, like the real valued spectrum. In this paper, we show how to find the closest reversible Markov chain to a given transition matrix. It turns out that this matrix can be computed by solving a convex minimization problem.

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Metadaten
Author:Adam Nielsen, Marcus Weber
Document Type:ZIB-Report
Tag:Convex Optimization; MSM; Reversible Markov Chain
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Date of first Publication:2014/12/10
Series (Serial Number):ZIB-Report (14-48)
ISSN:1438-0064