Rejoinder: ‘Network cross-validation by edge sampling’

Extract

1. Introduction

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.

2. Comparisons with other cross-validation approaches

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.