Learning Mixtures of Graphs from Epidemic Cascades

Jessica Hoffmann, Soumya Basu, Surbhi Goel, Constantine Caramanis
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:4342-4352, 2020.

Abstract

We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged. Graph mixtures are apparently no exception: until now, very little is known about whether this problem is solvable. To the best of our knowledge, we establish the first necessary and sufficient conditions for this problem to be solvable in polynomial time on edge-separated graphs. When the conditions are met, i.e., when the graphs are connected with at least three edges, we give an efficient algorithm for learning the weights of both graphs with optimal sample complexity (up to log factors). We give complementary results and provide sample-optimal (up to log factors) algorithms for mixtures of directed graphs of out-degree at least three, and for mixture of undirected graphs of unbalanced and/or unknown priors.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-hoffmann20a, title = {Learning Mixtures of Graphs from Epidemic Cascades}, author = {Hoffmann, Jessica and Basu, Soumya and Goel, Surbhi and Caramanis, Constantine}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {4342--4352}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/hoffmann20a/hoffmann20a.pdf}, url = { http://proceedings.mlr.press/v119/hoffmann20a.html }, abstract = {We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged. Graph mixtures are apparently no exception: until now, very little is known about whether this problem is solvable. To the best of our knowledge, we establish the first necessary and sufficient conditions for this problem to be solvable in polynomial time on edge-separated graphs. When the conditions are met, i.e., when the graphs are connected with at least three edges, we give an efficient algorithm for learning the weights of both graphs with optimal sample complexity (up to log factors). We give complementary results and provide sample-optimal (up to log factors) algorithms for mixtures of directed graphs of out-degree at least three, and for mixture of undirected graphs of unbalanced and/or unknown priors.} }
Endnote
%0 Conference Paper %T Learning Mixtures of Graphs from Epidemic Cascades %A Jessica Hoffmann %A Soumya Basu %A Surbhi Goel %A Constantine Caramanis %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-hoffmann20a %I PMLR %P 4342--4352 %U http://proceedings.mlr.press/v119/hoffmann20a.html %V 119 %X We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged. Graph mixtures are apparently no exception: until now, very little is known about whether this problem is solvable. To the best of our knowledge, we establish the first necessary and sufficient conditions for this problem to be solvable in polynomial time on edge-separated graphs. When the conditions are met, i.e., when the graphs are connected with at least three edges, we give an efficient algorithm for learning the weights of both graphs with optimal sample complexity (up to log factors). We give complementary results and provide sample-optimal (up to log factors) algorithms for mixtures of directed graphs of out-degree at least three, and for mixture of undirected graphs of unbalanced and/or unknown priors.
APA
Hoffmann, J., Basu, S., Goel, S. & Caramanis, C.. (2020). Learning Mixtures of Graphs from Epidemic Cascades. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:4342-4352 Available from http://proceedings.mlr.press/v119/hoffmann20a.html .

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