Accelerating convergence of inference in the inverse Ising problem

Inferring modelling parameters of dynamical processes from observational data is an important inverse problem in statistical physics. In this paper, instead of passively observing the dynamics for inference, we focus on strategically manipulating dynamics to generate data that gives more accurate estimators within fewer observations. For this purpose, we consider the inference problem rooted in the Ising model with two opposite external fields, assuming that the strength distribution of one of the fields (labelled as passive) is unknown and needs to be inferred. In contrast, the other field (labelled active) is strategically deployed to interact with the Ising dynamics in such a way as to improve the accuracy of estimates of inferring the opposing passive field. By comparing to benchmark cases, we first demonstrate that it is possible to accelerate the inference by strategically interacting with the Ising dynamics. We then apply series expansions to obtain an approximation of the optimized influence configurations in the high-temperature region. Furthermore, by using mean-field estimates, we also demonstrate the applicability of the method in a more general scenario where real-time tracking of the system is infeasible. Last, analysing the optimized influence profiles, we describe heuristics for manipulating the Ising dynamics for faster inference. For example, we show that agents targeted more strongly by the passive field should also be strongly targeted by the active one.