Dettmer, Simon L., Nguyen, H. Chau and Berg, Johannes (2016). Network inference in the nonequilibrium steady state. Phys. Rev. E, 94 (5). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2470-0053

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Abstract

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.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Dettmer, Simon L.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Nguyen, H. ChauUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Berg, JohannesUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-255792
DOI: 10.1103/PhysRevE.94.052116
Journal or Publication Title: Phys. Rev. E
Volume: 94
Number: 5
Date: 2016
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 2470-0053
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
MEAN-FIELD THEORY; BOLTZMANN MACHINES; ISING-MODEL; SPIN-GLASS; ALGORITHMMultiple languages
Physics, Fluids & Plasmas; Physics, MathematicalMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/25579

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