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2017 | 5 | 1 | 73-81
Tytuł artykułu

Finding metastabilities in reversible Markov chains based on incomplete sampling

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In order to fully characterize the state-transition behaviour of finite Markov chains one needs to provide the corresponding transition matrix P. In many applications such as molecular simulation and drug design, the entries of the transition matrix P are estimated by generating realizations of the Markov chain and determining the one-step conditional probability Pij for a transition from one state i to state j. This sampling can be computational very demanding. Therefore, it is a good idea to reduce the sampling effort. The main purpose of this paper is to design a sampling strategy, which provides a partial sampling of only a subset of the rows of such a matrix P. Our proposed approach fits very well to stochastic processes stemming from simulation of molecular systems or random walks on graphs and it is different from the matrix completion approaches which try to approximate the transition matrix by using a low-rank-assumption. It will be shown how Markov chains can be analyzed on the basis of a partial sampling. More precisely. First, we will estimate the stationary distribution from a partially given matrix P. Second, we will estimate the infinitesimal generator Q of P on the basis of this stationary distribution. Third, from the generator we will compute the leading invariant subspace, which should be identical to the leading invariant subspace of P. Forth, we will apply Robust Perron Cluster Analysis (PCCA+) in order to identify metastabilities using this subspace.
Wydawca
Czasopismo
Rocznik
Tom
5
Numer
1
Strony
73-81
Opis fizyczny
Daty
wydano
2017-01-01
otrzymano
2016-11-25
zaakceptowano
2017-03-16
online
2017-04-19
Twórcy
autor
  • Zuse Institute Berlin (ZIB), Takustr 7, 14195 Berlin,, weber@zib.de
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2017-0006
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