Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.

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逆统计问题：从逆伊辛问题到数据科学

统计物理学中的逆问题是由不同领域的“大数据”挑战所激发的，特别是生物学中的高通量实验。在反问题中，需要颠倒统计物理学的通常程序：我们不是根据模型参数计算可观测值，而是试图根据观测值推断模型的参数。在这篇综述中，我们关注逆伊辛问题和密切相关的问题，即如何在给定观察到的自旋相关性、磁化强度或其他数据的情况下推断自旋之间的耦合强度。我们回顾了逆伊辛问题的应用，包括神经连接的重建、蛋白质结构的确定和基因调控网络的推断。对于平衡中的逆伊辛问题，统计力学界已经开发了许多受控和非受控的近似解。一个特别强大的方法，伪似然，源于统计。我们还回顾了非平衡情况下的逆伊辛问题，其中模型参数必须基于非平衡统计来重建。