论推理模型的临界性
On the criticality of inferred models
摘要：
先进的推理技术允许人们从高维数据集重建相互作用的模式。在这里，我们专注于推断模型的统计特性，并认为推断程序可能会产生接近相变的模型。一方面，我们表明，在这些模型的概率分布的空间中的重新参数化不变度量（Fisher信息）是直接相关的模型的易感性。因此，可区分的模型往往积累接近临界点，在那里的磁化率发散在无限的系统。另一方面，该区域是推断参数的估计最稳定的区域。为了说明这些点，我们讨论了推理的相互作用点过程与应用程序的金融数据，并表明，明智的选择的观察时间尺度自然产生的模型是接近临界。
英文摘要：
Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to a phase transition. On one side, we show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher Information) is directly related to the model's susceptibility. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. On the other, this region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time-scales naturally yield models which are close to criticality.
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