Complex networks can be modeled as a probabilistic graphical model, where the interactions between binary variables, "spins", on nodes are described by a coupling matrix that is inferred from observations. The inverse statistical problem of finding direct interactions is difficult, especially for large systems, because of the exponential growth in the possible number of states and the possible number of networks . In the context of the experimental sciences, well-controlled perturbations can be applied to a system, shedding light on the internal structure of the network. Therefore, we propose a method to improve the accuracy and efficiency of inference by iteratively applying perturbations to a network that are advantageous under a Bayesian framework. The spectrum of the empirical Fisher information can be used as a measure for the difficulty of the inference during the training process. We significantly improve the accuracy and efficiency of inference in medium-sized networks based on this strategy with a reasonable number of experimental queries . Our method could be powerful in the analysis of complex networks as well as in the rational design of experiments.
 The inverse statistical problem of finding direct interactions in complex networks is difficult . In the context of the experimental sciences, well-controlled perturbations can be applied to a system, probing the internal structure of the network. Therefore, we propose a general mathematical framework to study inference with iteratively applied perturbations to a network . Formulating active learning in the language of information geometry, our framework quantifies the difficulty of inference as well as the information gain due to perturbations through the curvature of the underlying parameter manifold as measured though the empirical Fisher information . Perturbations are then chosen that reduce most the variance of the Bayesian posterior. We apply this framework to a specific probabilistic graphical model where the nodes in the network are modeled as binary variables, "spins" with Ising-form pairwise interactions. Based on this strategy, we significantly improve the accuracy and efficiency of inference from a reasonable number of experimental queries for medium sized networks. Our active learning framework could be powerful in the analysis of complex networks as well as in the rational design of experiments.
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can be used as a measure for the difficulty of the inference during the training process. We
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