2022/11/20 by Arash Amini, Qiyu Sun, Amini, Arash +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #47H25 (Secondary) #93E35 (Primary) 93B70 #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Gene Regulatory Network Analysis #Machine Learning (cs.LG) #Markov Chains and Monte Carlo Methods #Statistics Theory (math.ST) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2211.11069
openalex publication_date 2022/11/20 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28
We consider a class of stochastic dynamical networks whose governing dynamics can be modeled using a coupling function. It is shown that the dynamics of such networks can generate geometrically ergodic trajectories under some reasonable assumptions. We show that a general class of coupling functions can be learned using only one sample trajectory from the network. This is practically plausible as in numerous applications it is desired to run an experiment only once but for a longer period of time, rather than repeating the same experiment multiple times from different initial conditions. Building upon ideas from the concentration inequalities for geometrically ergodic Markov chains, we formulate several results about the convergence of the empirical estimator to the true coupling function. Our theoretical findings are supported by extensive simulation results.