Discussion of ‘Network cross-validation by edge sampling’
《通过边抽样进行网络交叉验证》的讨论AI 解读 ↓
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《通过边抽样进行网络交叉验证》的讨论
- 研究问题
- 这篇讨论关注网络边抽样交叉验证的多折实现，以及它与块抽样方法在验证数据利用方式和估计误差上的可能差异。
- 方法与思路
- 讨论者比较边抽样与块抽样中节点对进入验证集的方式，并提出验证样本利用效率可能解释两者经验表现差异。
- 材料陈述的贡献
- 所给文字提出一种解释：边抽样更充分利用节点对进行验证；误差差异可能体现在常数层面，这是讨论判断而非已证明结论。
- 阅读关注点
- 应结合主论文核对两种抽样方法的实现和比较设置，区分讨论者的推测、主论文的模拟发现与已建立的理论结果。
- 阅读边界
- 所给材料为 OpenAlex 索引的讨论文本，稿件版本未注明；不能将其意见当作主论文定理，也不能据此确认收敛率相同。
原文摘要
We congratulate the authors for a nice contribution to the literature on model selection and assessment for complex network data. The article of Li et al. (2020) enriches the collection of tools available for network data analysis, bringing together different fields such as low-rank matrix estimation, cross-validation and network modelling. This discussion will focus on the |$V$|-fold variant of the edge sampling cross-validation method and its combination with other recently developed cross-validation methods and network models. |$V$|-fold cross-validation is perhaps the most popular variant of cross-validation. It partitions the training set into |$V$| disjoint folds and performs sample splitting validation by leaving out each fold as the validation set and using the remaining |$V-1$| folds for estimation. The final validated risk is obtained by aggregating the sample splitting validation risks over the folds. This idea can be extended straightforwardly to the edge sampling cross-validation framework, as mentioned in § 2.2 of Li et al. (2020). A related cross-validation method for network and other low-rank matrix estimation problems is the block sampling method developed by Chen & Lei (2018), where the sample splitting is realized by holding out a diagonal sub-block of the adjacency matrix. The simulation study in Li et al. (2020) includes some empirical comparisons between edge sampling and block sampling under various settings, and suggests that edge sampling may be preferable in more challenging settings. Given the nature of these algorithms, it is hard to imagine a difference in rates of convergence of the estimation error, and it seems more likely that the estimation errors would differ at a constant factor level. A possible explanation is the more efficient use of validation sample points in edge sampling. In |$V$|-fold edge sampling, each node pair appears exactly once as a validation sample point, so that the validation sample size is roughly |$n^2/2$|. In |$V$|-fold block sampling, on the other hand, only the node pairs in the diagonal sub-blocks are used for validation; hence the validation sample size for |$V$|-fold block sampling is approximately |$n^2/(2V)$|.