Tianxi Li’s contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu
Tianxi Li 对《网络潜在生长过程的根节点与社群推断》的讨论AI 解读 ↓
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Tianxi Li 对《网络潜在生长过程的根节点与社群推断》的讨论
- 研究问题
- 这篇讨论关注如何扩展优先连接树加随机噪声边的 PAPER 模型，以及相关根节点推断能否用于更一般的扩散网络。
- 方法与思路
- 作者从边层面与节点层面的信号加噪声结构出发，讨论模型组合、传递性扩展，并比较树生长与固定网络扩散两种设定。
- 材料陈述的贡献
- 所给摘要提出模型拓扑性质与扩散根节点推断的后续问题，并指出均匀噪声机制改变后，推断计算可能面临新的困难。
- 阅读关注点
- 应区分评论中的猜想、研究建议与主论文结果，核对两种网络设定重合的条件，以及根节点计算对均匀噪声边的依赖。
- 阅读边界
- 这是讨论文章的 OpenAlex 索引摘要，版本未注明；扩展与最优推断多为待研究问题，不能当作主论文已证明的结果。
原文摘要
I want to congratulate Prof. Crane and Prof. Xu for their impressive work. The paper introduces two novel components: the PAPER model and the inference framework for the tree. Both of them bring many insights into handling complex network data and open the doors to new problems. I will discuss extension problems from both aspects. The PAPER model assumes preferential attachment trees with additional the Erdős-Rényi (ER) edges. One nice property of the model lies in its ability to generate pendants that can often be observed in many real-world networks. The model can be interpreted as a signal (tree) + noise (ER) structure for edges. The recent core-periphery models of Elliott et al. (2020) and Miao and Li (2023) can be seen as examples of such a structure at the node level. It would be interesting to see what could be achieved by combining the two signal+noise structures. Meanwhile, the topological properties of PAPER are also worth a thorough study. For example, as both tree structures and the ER model lack transitivity, we may conjecture that the PAPER also has the same limitation. How to generalize the model to incorporate such additional properties would be an important direction for future research. One potential obstacle to such generalization might be the root inference computation. The paper’s inference nicely hinges on the uniform noise edges in the ER mechanism, and it is unclear if the computation can be efficiently done without it. A related setting for root inference is the diffusion scenario, which was initially studied in Shah and Zaman (2011) with many follow-up studies (Dawkins et al., 2021; Kazemitabar & Amini, 2020; Khim & Loh, 2016): a fixed network (not necessarily a tree) is given and a random diffusion process is initiated within the network. This diffusion scenario differs from the tree-growing setting, but when the network in the former is a tree and the ER part is removed from PAPER (Crane & Xu, 2021), the two settings coincide. The setup of the current paper is not directly compatible with the diffusion setting. Still, the available optimality in the tree-growing scenario raises a natural question about whether we can build an optimal inference procedure in the diffusion setting. Defining a similar inference method seems plausible, but the computation is again a bottleneck. Explorations in this direction may help with broader applications in epidemiology and cyber security.