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.

翻译：我们考虑的是一组随机动态网络,其管理动态可以使用组合功能进行模拟,显示这些网络的动态可以在某些合理的假设下产生几何性电子轨迹。我们显示,只有利用网络的一个样本轨迹才能学到一般的组合功能。这实际上是合理的,因为在许多应用中,它只希望进行一次实验,但需要更长的时间,而不是从不同的初始条件重复多次同样的实验。我们根据从几何性ergodic Markov 链条的集中性不平等中得出的设想,就经验估计器与真正的组合功能的融合得出若干结果。我们的理论结论得到广泛的模拟结果的支持。