Repository: Freie Universität Berlin, Math Department

Variational approach for learning Markov processes from time series data

Wu, Ho and Noé, Frank (2019) Variational approach for learning Markov processes from time series data. Journal of Nonlinear Science, 30 . pp. 23-66. ISSN 1432-1467 (online)

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Inference, prediction, and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly nonlinear dynamical systems is facilitated by the fact that we can often find a (generally nonlinear) transformation of the system coordinates to features in which the dynamics can be excellently approximated by a linear Markovian model. Moreover, the large number of system variables often change collectively on large time- and length-scales, facilitating a low-dimensional analysis in feature space. In this paper, we introduce a variational approach for Markov processes (VAMP) that allows us to find optimal feature mappings and optimal Markovian models of the dynamics from given time series data. The key insight is that the best linear model can be obtained from the top singular components of the Koopman operator. This leads to the definition of a family of score functions called VAMP-r which can be calculated from data, and can be employed to optimize a Markovian model. In addition, based on the relationship between the variational scores and approximation errors of Koopman operators, we propose a new VAMP-E score, which can be applied to cross-validation for hyper-parameter optimization and model selection in VAMP. VAMP is valid for both reversible and nonreversible processes and for stationary and nonstationary processes or realizations.

Item Type:Article
Subjects:Physical Sciences
Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Mathematical and Computer Sciences > Artificial Intelligence > Machine Learning
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2091
Deposited By: BioComp Admin
Deposited On:25 Sep 2017 21:22
Last Modified:11 Feb 2022 13:08

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