Garlaschelli Diego, Loffredo Maria I
Dipartimento di Fisica, Università di Siena, Via Roma 56, 53100 Siena, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):015101. doi: 10.1103/PhysRevE.78.015101. Epub 2008 Jul 28.
The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the maximum likelihood (ML) principle indicates a unique, statistically rigorous parameter choice, associated with a well-defined topological feature. We then find that, if the ML condition is incompatible with the built-in parameter choice, network models turn out to be intrinsically ill defined or biased. To overcome this problem, we construct a class of safely unbiased models. We also propose an extension of these results that leads to the fascinating possibility to extract, only from topological data, the "hidden variables" underlying network organization, making them "no longer hidden." We test our method on World Trade Web data, where we recover the empirical gross domestic product using only topological information.
网络模型中自由参数的选择是主观的，因为这取决于所监测的拓扑属性。然而，我们表明最大似然（ML）原理指示了一种独特的、统计上严格的参数选择，它与一个定义明确的拓扑特征相关联。然后我们发现，如果最大似然条件与内置参数选择不兼容，网络模型最终会本质上定义不明确或有偏差。为了克服这个问题，我们构建了一类安全无偏差的模型。我们还提出了这些结果的一种扩展，这带来了一种引人入胜的可能性，即仅从拓扑数据中提取网络组织背后的“隐藏变量”，使其“不再隐藏”。我们在世界贸易网络数据上测试了我们的方法，在该数据中我们仅使用拓扑信息就恢复了实际国内生产总值。
