Network Growth Models such as Preferential Attachment and Duplication/Divergence are popular generative models with which to study complex networks in biology, sociology, and computer science. However, analyzing them within the framework of model selection and statistical inference is often complicated and computationally difficult, particularly when comparing models that are not directly related or nested. In practice, ad hoc methods are often used with uncertain results. If possible, the use of standard likelihood-based statistical model selection techniques is desirable.With this in mind, we develop an Adaptive Importance Sampling algorithm for estimating likelihoods of Network Growth Models. We introduce the use of the classic Plackett-Luce model of rankings as a family of importance distributions. Updates to importance distributions are performed iteratively via the Cross-Entropy Method with an additional correction for degeneracy/over-fitting inspired by the Minimum Description Length principle. This correction can be applied to other estimation problems using the Cross-Entropy method for integration/approximate counting, and it provides an interpretation of Adaptive Importance Sampling as iterative model selection. Empirical results for the Preferential Attachment model are given, along with a comparison to an alternative established technique, Annealed Importance Sampling.

中文翻译：

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网络增长模型的自适应重要性采样

偏好依附和重复/发散等网络增长模型是研究生物学、社会学和计算机科学中复杂网络的流行生成模型。然而，在模型选择和统计推断的框架内分析它们通常很复杂且计算困难，特别是在比较不直接相关或嵌套的模型时。在实践中，临时方法经常用于结果不确定的情况。如果可能，最好使用基于标准似然的统计模型选择技术。考虑到这一点，我们开发了一种自适应重要性采样算法来估计网络增长模型的似然性。我们介绍使用经典的 Plackett-Luce 排名模型作为重要性分布族。重要性分布的更新通过交叉熵方法迭代执行，并在最小描述长度原则的启发下对退化/过拟合进行额外校正。这种校正可以应用于使用交叉熵方法进行积分/近似计数的其他估计问题，并且它将自适应重要性采样解释为迭代模型选择。给出了优先依恋模型的实证结果，并与另一种已建立的技术，退火重要性采样进行了比较。这种校正可以应用于使用交叉熵方法进行积分/近似计数的其他估计问题，并且它将自适应重要性采样解释为迭代模型选择。给出了优先依恋模型的实证结果，并与另一种已建立的技术，退火重要性采样进行了比较。这种校正可以应用于使用交叉熵方法进行积分/近似计数的其他估计问题，并且它将自适应重要性采样解释为迭代模型选择。给出了优先依恋模型的实证结果，并与另一种已建立的技术，退火重要性采样进行了比较。