Network inference in the nonequilibrium steady state

Nonequilibrium systems lack an explicit characterization of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of the parameters of a model when its dynamics lacks detailed balance. Such nonequilibrium systems occur naturally i...

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Vydané v:Physical review. E Ročník 94; číslo 5-1; s. 052116
Hlavní autori: Dettmer, Simon L, Nguyen, H Chau, Berg, Johannes
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States 01.11.2016
ISSN:2470-0053, 2470-0053
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Shrnutí:Nonequilibrium systems lack an explicit characterization of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of the parameters of a model when its dynamics lacks detailed balance. Such nonequilibrium systems occur naturally in applications like neural networks and gene regulatory networks. Here, we focus on the paradigmatic asymmetric Ising model and show that we can learn its parameters from independent samples of the nonequilibrium steady state. We present both an exact inference algorithm and a computationally more efficient, approximate algorithm for weak interactions based on a systematic expansion around mean-field theory. Obtaining expressions for magnetizations and two- and three-point spin correlations, we establish that these observables are sufficient to infer the model parameters. Further, we discuss the symmetries characterizing the different orders of the expansion around the mean field and show how different types of dynamics can be distinguished on the basis of samples from the nonequilibrium steady state.
Bibliografia:ObjectType-Article-1
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ISSN:2470-0053
2470-0053
DOI:10.1103/PhysRevE.94.052116