TY - JOUR

T1 - Analysis of the Identifying Regulation With Adversarial Surrogates Algorithm

AU - Teichner, Ron

AU - Meir, Ron

AU - Margaliot, Michael

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2024

Y1 - 2024

N2 - Given a time-series zk k=1 N of noisy measured outputs along a single trajectory of a dynamical system, the Identifying Regulation with Adversarial Surrogates (IRAS) algorithm aims to find a non-trivial first integral of the system, that is, a scalar function g such that g (zi) g(zj) , for all i, j. IRAS has been suggested recently and was used successfully in several learning tasks in models from biology and physics. Here, we give the first rigorous analysis of this algorithm in a specific setting. We assume that the observations admit a linear first integral and that they are contaminated by Gaussian noise. We show that in this case the IRAS iterations are closely related to the self-consistent-field (SCF) iterations for solving a generalized Rayleigh quotient minimization problem. Using this approach, we derive several sufficient conditions guaranteeing local convergence of IRAS to the linear first integral.

AB - Given a time-series zk k=1 N of noisy measured outputs along a single trajectory of a dynamical system, the Identifying Regulation with Adversarial Surrogates (IRAS) algorithm aims to find a non-trivial first integral of the system, that is, a scalar function g such that g (zi) g(zj) , for all i, j. IRAS has been suggested recently and was used successfully in several learning tasks in models from biology and physics. Here, we give the first rigorous analysis of this algorithm in a specific setting. We assume that the observations admit a linear first integral and that they are contaminated by Gaussian noise. We show that in this case the IRAS iterations are closely related to the self-consistent-field (SCF) iterations for solving a generalized Rayleigh quotient minimization problem. Using this approach, we derive several sufficient conditions guaranteeing local convergence of IRAS to the linear first integral.

KW - Rayleigh quotient

KW - eigenvalue problems

KW - learning algorithms

KW - ribosome flow model

KW - self-consistent-field iteration

UR - http://www.scopus.com/inward/record.url?scp=85193252132&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2024.3400697

DO - 10.1109/LCSYS.2024.3400697

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AN - SCOPUS:85193252132

SN - 2475-1456

VL - 8

SP - 592

EP - 597

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -