On the Theoretical Properties of the Network Jackknife

Qiaohui Lin, Robert Lunde, Purnamrita Sarkar
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:6105-6115, 2020.

Abstract

We study the properties of a leave-node-out jackknife procedure for network data. Under the sparse graphon model, we prove an Efron-Stein-type inequality, showing that the network jackknife leads to conservative estimates of the variance (in expectation) for any network functional that is invariant to node permutation. For a general class of count functionals, we also establish consistency of the network jackknife. We complement our theoretical analysis with a range of simulated and real-data examples and show that the network jackknife offers competitive performance in cases where other resampling methods are known to be valid. In fact, for several network statistics, we see that the jackknife provides more accurate inferences compared to related methods such as subsampling.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-lin20c, title = {On the Theoretical Properties of the Network Jackknife}, author = {Lin, Qiaohui and Lunde, Robert and Sarkar, Purnamrita}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {6105--6115}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/lin20c/lin20c.pdf}, url = {https://proceedings.mlr.press/v119/lin20c.html}, abstract = {We study the properties of a leave-node-out jackknife procedure for network data. Under the sparse graphon model, we prove an Efron-Stein-type inequality, showing that the network jackknife leads to conservative estimates of the variance (in expectation) for any network functional that is invariant to node permutation. For a general class of count functionals, we also establish consistency of the network jackknife. We complement our theoretical analysis with a range of simulated and real-data examples and show that the network jackknife offers competitive performance in cases where other resampling methods are known to be valid. In fact, for several network statistics, we see that the jackknife provides more accurate inferences compared to related methods such as subsampling.} }
Endnote
%0 Conference Paper %T On the Theoretical Properties of the Network Jackknife %A Qiaohui Lin %A Robert Lunde %A Purnamrita Sarkar %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-lin20c %I PMLR %P 6105--6115 %U https://proceedings.mlr.press/v119/lin20c.html %V 119 %X We study the properties of a leave-node-out jackknife procedure for network data. Under the sparse graphon model, we prove an Efron-Stein-type inequality, showing that the network jackknife leads to conservative estimates of the variance (in expectation) for any network functional that is invariant to node permutation. For a general class of count functionals, we also establish consistency of the network jackknife. We complement our theoretical analysis with a range of simulated and real-data examples and show that the network jackknife offers competitive performance in cases where other resampling methods are known to be valid. In fact, for several network statistics, we see that the jackknife provides more accurate inferences compared to related methods such as subsampling.
APA
Lin, Q., Lunde, R. & Sarkar, P.. (2020). On the Theoretical Properties of the Network Jackknife. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:6105-6115 Available from https://proceedings.mlr.press/v119/lin20c.html.

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