Nonparametric Embeddings of Sparse High-Order Interaction Events

Zheng Wang, Yiming Xu, Conor Tillinghast, Shibo Li, Akil Narayan, Shandian Zhe
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:23237-23253, 2022.

Abstract

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound ) of the sparse ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-wang22ah, title = {Nonparametric Embeddings of Sparse High-Order Interaction Events}, author = {Wang, Zheng and Xu, Yiming and Tillinghast, Conor and Li, Shibo and Narayan, Akil and Zhe, Shandian}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {23237--23253}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/wang22ah/wang22ah.pdf}, url = {https://proceedings.mlr.press/v162/wang22ah.html}, abstract = {High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound ) of the sparse ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.} }
Endnote
%0 Conference Paper %T Nonparametric Embeddings of Sparse High-Order Interaction Events %A Zheng Wang %A Yiming Xu %A Conor Tillinghast %A Shibo Li %A Akil Narayan %A Shandian Zhe %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-wang22ah %I PMLR %P 23237--23253 %U https://proceedings.mlr.press/v162/wang22ah.html %V 162 %X High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound ) of the sparse ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.
APA
Wang, Z., Xu, Y., Tillinghast, C., Li, S., Narayan, A. & Zhe, S.. (2022). Nonparametric Embeddings of Sparse High-Order Interaction Events. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:23237-23253 Available from https://proceedings.mlr.press/v162/wang22ah.html.

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