Active Learning of Spin Network Models

The inverse statistical problem of finding direct interactions in complex networks is difficult. In the natural sciences, well-controlled perturbation experiments are widely used to probe the structure of complex networks. However, our understanding of how and why perturbations aid inference remains heuristic, and we lack automated procedures that determine network structure by combining inference and perturbation. Therefore, we propose a general mathematical framework to study inference with iteratively applied perturbations. Using the formulation of information geometry, our framework quantifies the difficulty of inference and the information gain from perturbations through the curvature of the underlying parameter manifold, measured by Fisher information. We apply the framework to the inference of spin network models and find that designed perturbations can reduce the sampling complexity by $10^6$-fold across a variety of network architectures. Physically, our framework reveals that perturbations boost inference by causing a network to explore previously inaccessible states. Optimal perturbations break spin-spin correlations within a network, increasing the information available for inference and thus reducing sampling complexity by orders of magnitude. Our active learning framework could be powerful in the analysis of complex networks as well as in the rational design of experiments.