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, magnetisations, 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.

该文章介绍了逆向问题在统计物理学中的应用，特别是在生物学领域的大规模数据中的应用，重点关注逆向伊辛问题及其应用，通过给定观测自旋相关性、磁化或其他数据，推断自旋之间的耦合强度。文章回顾了伊辛问题的应用，包括神经连接重建，蛋白质结构测定和基因调控网络的推断。在统计力学社区中，已经开发了许多控制和非控制逼近方法，包括拟似似然方法等。此外，文章还介绍了非平衡问题中的伊辛问题，其中必须根据非平衡统计学重建模型参数。