Graph Mixture Density Networks

Federico Errica, Davide Bacciu, Alessio Micheli
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:3025-3035, 2021.

Abstract

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph representation learning, we address a broader class of challenging conditional density estimation problems that rely on structured data. In this respect, we evaluate our method on a new benchmark application that leverages random graphs for stochastic epidemic simulations. We show a significant improvement in the likelihood of epidemic outcomes when taking into account both multimodality and structure. The empirical analysis is complemented by two real-world regression tasks showing the effectiveness of our approach in modeling the output prediction uncertainty. Graph Mixture Density Networks open appealing research opportunities in the study of structure-dependent phenomena that exhibit non-trivial conditional output distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-errica21a, title = {Graph Mixture Density Networks}, author = {Errica, Federico and Bacciu, Davide and Micheli, Alessio}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {3025--3035}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/errica21a/errica21a.pdf}, url = {https://proceedings.mlr.press/v139/errica21a.html}, abstract = {We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph representation learning, we address a broader class of challenging conditional density estimation problems that rely on structured data. In this respect, we evaluate our method on a new benchmark application that leverages random graphs for stochastic epidemic simulations. We show a significant improvement in the likelihood of epidemic outcomes when taking into account both multimodality and structure. The empirical analysis is complemented by two real-world regression tasks showing the effectiveness of our approach in modeling the output prediction uncertainty. Graph Mixture Density Networks open appealing research opportunities in the study of structure-dependent phenomena that exhibit non-trivial conditional output distributions.} }
Endnote
%0 Conference Paper %T Graph Mixture Density Networks %A Federico Errica %A Davide Bacciu %A Alessio Micheli %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-errica21a %I PMLR %P 3025--3035 %U https://proceedings.mlr.press/v139/errica21a.html %V 139 %X We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph representation learning, we address a broader class of challenging conditional density estimation problems that rely on structured data. In this respect, we evaluate our method on a new benchmark application that leverages random graphs for stochastic epidemic simulations. We show a significant improvement in the likelihood of epidemic outcomes when taking into account both multimodality and structure. The empirical analysis is complemented by two real-world regression tasks showing the effectiveness of our approach in modeling the output prediction uncertainty. Graph Mixture Density Networks open appealing research opportunities in the study of structure-dependent phenomena that exhibit non-trivial conditional output distributions.
APA
Errica, F., Bacciu, D. & Micheli, A.. (2021). Graph Mixture Density Networks. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:3025-3035 Available from https://proceedings.mlr.press/v139/errica21a.html.

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