Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks
Sampling and Inference for Beta Neutral-to-the-Left Models of Sparse Networks
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发表时间：
2018-07
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通讯作者：
Benjamin Bloem-Reddy;Adam Foster;Emile Mathieu;Y. Teh
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作者：
Benjamin Bloem-Reddy;Adam Foster;Emile Mathieu;Y. Teh
经验证据表明，许多真实网络中出现的重尾度分布可以通过指数 $\eta$ 的幂律很好地逼近，其值可以小于或大于 2。基于各种形式的可交换性的模型能够捕获 $\eta 2$ 的幂律，而现有随机图模型中使用的可交换性形式无法生成该幂律。优先依恋模型生成大于二的幂律指数，但由于在不可交换模型中执行推理的固有困难，其作为统计模型的用途有限。受这一差距的启发，我们为最近提出的一类模型设计并实现了推理算法，该模型生成所有可能值的 $\eta$。我们表明，尽管它们不可互换，但这些模型具有易于推理的概率结构。我们的方法使一大类以前难以处理的模型可用于统计推断。
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various forms of exchangeability are able to capture power laws with $\eta 2$ cannot be generated by the forms of exchangeability used in existing random graph models. Preferential attachment models generate power law exponents greater than two, but have been of limited use as statistical models due to the inherent difficulty of performing inference in non-exchangeable models. Motivated by this gap, we design and implement inference algorithms for a recently proposed class of models that generates $\eta$ of all possible values. We show that although they are not exchangeable, these models have probabilistic structure amenable to inference. Our methods make a large class of previously intractable models useful for statistical inference.