Due to the interconnectedness of financial entities, estimating certain key properties of a complex financial system (e.g. the implied level of systemic risk) requires detailed information about the structure of the underlying network. However, since data about financial linkages are typically subject to confidentiality, network reconstruction techniques become necessary to infer both the presence of connections and their intensity. Recently, several "horse races" have been conducted to compare the performance of the available financial network reconstruction methods. These comparisons, however, were based on arbitrarily-chosen similarity metrics between the real and the reconstructed network. Here we establish a generalised maximum-likelihood approach to rigorously define and compare weighted reconstruction methods. Our generalization maximizes the conditional entropy to solve the problem represented by the fact that the density-dependent constraints required to reliably reconstruct the network are typically unobserved. The resulting approach admits as input any reconstruction method for the purely binary topology and, conditionally on the latter, exploits the available partial information to infer link weights. We find that the most reliable method is obtained by "dressing" the best-performing binary method with an exponential distribution of link weights having a properly density-corrected and link-specific mean value and propose two unbiased (in the sense of maximum conditional entropy) variants of it. While the one named CReMA is perfectly general (as a particular case, it can place optimal weights on a network whose topology is known), the one named CReMB is recommended both in case of full uncertainty about the network topology and if the existence of some links is certain. In these cases, the CReMB is faster and reproduces empirical networks with highest generalised likelihood.

中文翻译：

---

更安全的道路上的更快的马：加权网络有效重建的广义推理

由于金融实体的相互联系，估计复杂金融系统的某些关键属性（例如系统性风险的隐含水平）需要有关底层网络结构的详细信息。然而，由于有关金融联系的数据通常需要保密，因此需要网络重建技术来推断联系的存在及其强度。最近，已经进行了几次“赛马”来比较可用的金融网络重建方法的性能。然而，这些比较是基于真实网络和重建网络之间任意选择的相似性度量。在这里，我们建立了一种广义的最大似然方法来严格定义和比较加权重建方法。我们的泛化最大化了条件熵，以解决由以下事实表示的问题：可靠地重建网络所需的密度相关约束通常是未观察到的。由此产生的方法允许纯二元拓扑的任何重建方法作为输入，并且在后者的条件下，利用可用的部分信息来推断链接权重。我们发现最可靠的方法是通过“修饰”性能最佳的二进制方法获得的，链接权重的指数分布具有适当的密度校正和链接特定的平均值，并提出了两个无偏（在最大条件熵的意义上） ) 的变种。虽然名为 CReMA 的是完全通用的（作为一种特殊情况，它可以在拓扑已知的网络上放置最佳权重），在网络拓扑完全不确定的情况下以及某些链接的存在是确定的情况下，都建议使用名为 CReMB 的方法。在这些情况下，CReMB 速度更快，并以最高的广义似然再现经验网络。