投影、稀疏且可学习的潜在位置网络模型
Projective, Sparse, and Learnable Latent Position Network Models
AI总结：
本文针对稀疏网络建模中传统独立同分布假设导致平均度线性增长的问题，提出基于泊松点过程生成潜在位置的投影稀疏潜在位置模型，并给出潜在位置一致估计的条件。
摘要：
在使用潜在位置模型对网络数据进行建模时，通常假设节点的位置是独立同分布的。然而，这一假设意味着平均节点度随节点数量线性增长，这在图被认为是稀疏的情况下并不合适。我们提出一种替代假设——潜在位置按照泊松点过程生成——并证明它与不同程度的稀疏性兼容。与文献中其他稀疏潜在位置模型的概念不同，我们的框架还定义了一个投影的概率模型序列，从而确保在不同规模网络之间统计推断的一致性。我们建立了潜在位置一致估计的条件，并将我们的结果与现有的稀疏网络建模框架进行了比较。
英文摘要：
When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the number of nodes, which is inappropriate when the graph is thought to be sparse. We propose an alternative assumption -- that the latent positions are generated according to a Poisson point process -- and show that it is compatible with various levels of sparsity. Unlike other notions of sparse latent position models in the literature, our framework also defines a projective sequence of probability models, thus ensuring consistency of statistical inference across networks of different sizes. We establish conditions for consistent estimation of the latent positions, and compare our results to existing frameworks for modeling sparse networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
