Rejoinder: ‘Network cross-validation by edge sampling’
《基于边抽样的网络交叉验证》讨论回复AI 解读 ↓
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《基于边抽样的网络交叉验证》讨论回复
- 研究问题
- 边抽样网络交叉验证与先前方法的表现为何不同？这篇回复讨论收敛速率猜想、验证集有效规模和孤立节点的作用。
- 方法与思路
- 作者回应讨论者意见，提供澄清、评论及部分数值结果，并从训练集和验证集结构解释边抽样与节点抽样的差别。
- 材料陈述的贡献
- 摘要提出边抽样较不易产生无助于拟合的孤立节点，并赞同两种方法速率可能相同的猜想；这里并未报告该猜想的证明。
- 阅读关注点
- 应结合主论文与讨论核对抽样方案、有效验证集规模及数值比较，特别区分已证明的结论、经验解释与尚待证明的猜想。
- 阅读边界
- 这是讨论回复，不能替代主论文。所给OpenAlex索引摘要未注明稿件版本，速率相同仅为猜想，数值结果细节未提供。
原文摘要
We thank the editor for organizing this discussion and giving us the opportunity to read experts’ perspectives on our work. We are grateful to all the discussants for their insightful contributions, which raise many important points and offer suggestions for potential improvements and generalizations of our method. In this rejoinder we provide some clarifications, remarks and selected numerical results in response to these comments. Lei & Lin (2020) conjecture, and we agree, that the rates of our proposed edge cross-validation method and the earlier proposal of Chen & Lei (2018), referred to as network cross-validation in the paper, are very likely the same, up to perhaps a constant. They make the interesting observation that one reason for the difference in performance we observed could be the effective size of the validation set under edge sampling. This points to another related feature of our sampling scheme, which is reflected in the training set as well: sampling edges, as we do, is less likely to create isolated nodes than sampling nodes would, and isolated nodes provide no information for model fitting and are thus useless in training.