A Flexible Latent Space Model for Multilayer Networks

Xuefei Zhang, Songkai Xue, Ji Zhu
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:11288-11297, 2020.

Abstract

Entities often interact with each other through multiple types of relations, which are often represented as multilayer networks. Multilayer networks among the same set of nodes usually share common structures, while each layer can possess its distinct node connecting behaviors. This paper proposes a flexible latent space model for multilayer networks for the purpose of capturing such characteristics. Specifically, the proposed model embeds each node with a latent vector shared among layers and a layer-specific effect for each layer; both elements together with a layer-specific connectivity matrix determine edge formations. To fit the model, we develop a projected gradient descent algorithm for efficient parameter estimation. We also establish theoretical properties of the maximum likelihood estimators and show that the upper bound of the common latent structure’s estimation error is inversely proportional to the number of layers under mild conditions. The superior performance of the proposed model is demonstrated through simulation studies and applications to two real-world data examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-zhang20aa, title = {A Flexible Latent Space Model for Multilayer Networks}, author = {Zhang, Xuefei and Xue, Songkai and Zhu, Ji}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {11288--11297}, 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/zhang20aa/zhang20aa.pdf}, url = {https://proceedings.mlr.press/v119/zhang20aa.html}, abstract = {Entities often interact with each other through multiple types of relations, which are often represented as multilayer networks. Multilayer networks among the same set of nodes usually share common structures, while each layer can possess its distinct node connecting behaviors. This paper proposes a flexible latent space model for multilayer networks for the purpose of capturing such characteristics. Specifically, the proposed model embeds each node with a latent vector shared among layers and a layer-specific effect for each layer; both elements together with a layer-specific connectivity matrix determine edge formations. To fit the model, we develop a projected gradient descent algorithm for efficient parameter estimation. We also establish theoretical properties of the maximum likelihood estimators and show that the upper bound of the common latent structure’s estimation error is inversely proportional to the number of layers under mild conditions. The superior performance of the proposed model is demonstrated through simulation studies and applications to two real-world data examples.} }
Endnote
%0 Conference Paper %T A Flexible Latent Space Model for Multilayer Networks %A Xuefei Zhang %A Songkai Xue %A Ji Zhu %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-zhang20aa %I PMLR %P 11288--11297 %U https://proceedings.mlr.press/v119/zhang20aa.html %V 119 %X Entities often interact with each other through multiple types of relations, which are often represented as multilayer networks. Multilayer networks among the same set of nodes usually share common structures, while each layer can possess its distinct node connecting behaviors. This paper proposes a flexible latent space model for multilayer networks for the purpose of capturing such characteristics. Specifically, the proposed model embeds each node with a latent vector shared among layers and a layer-specific effect for each layer; both elements together with a layer-specific connectivity matrix determine edge formations. To fit the model, we develop a projected gradient descent algorithm for efficient parameter estimation. We also establish theoretical properties of the maximum likelihood estimators and show that the upper bound of the common latent structure’s estimation error is inversely proportional to the number of layers under mild conditions. The superior performance of the proposed model is demonstrated through simulation studies and applications to two real-world data examples.
APA
Zhang, X., Xue, S. & Zhu, J.. (2020). A Flexible Latent Space Model for Multilayer Networks. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:11288-11297 Available from https://proceedings.mlr.press/v119/zhang20aa.html.

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