We propose a novel approach to the inverse Ising problem which employs the recently introduced density consistency approximation (DC) to determine the model parameters (couplings and external fields) maximizing the likelihood of given empirical data. This method allows for closed-form expressions of the inferred parameters as a function of the first and second empirical moments. Such expressions have a similar structure to the small-correlation expansion derived in reference Sessak and Monasson (2009 J. Phys. A: Math. Theor. 42 055001), of which they provide an improvement in the case of non-zero magnetization at low temperatures, as well as in presence of random external fields. The present work provides an extensive comparison with most common inference methods used to reconstruct the model parameters in several regimes, i.e. by varying both the network topology and the distribution of fields and couplings. The comparison shows that no method is uniformly better than every other one, but DC appears nevertheless as one of the most accurate and reliable approaches to infer couplings and fields from first and second moments in a significant range of parameters.

我们提出了一种解决逆伊辛问题的新方法，该方法采用最近引入的密度一致性近似 (DC) 来确定模型参数（耦合和外部场），从而最大化给定经验数据的可能性。该方法允许将推断参数的闭式表达式作为第一和第二经验矩的函数。此类表达式与参考 Sessak 和 Monasson (2009 J. Phys. A: Math. Theor. 42) 中导出的小相关扩展具有相似的结构055001），其中它们在低温下非零磁化以及存在随机外部场的情况下提供了改进。目前的工作提供了与最常见的推理方法的广泛比较，用于在几种情况下重建模型参数，即通过改变网络拓扑以及场和耦合的分布。比较表明，没有任何一种方法比其他任何一种方法都更好，但 DC 仍然是最准确、最可靠的方法之一，可以在很大的参数范围内从一阶矩和二阶矩推断耦合和场。