Parameter Estimation in DAGs from Incomplete Data via Optimal Transport

Vy Vo, Trung Le, Long Tung Vuong, He Zhao, Edwin V. Bonilla, Dinh Phung
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:49580-49604, 2024.

Abstract

Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the versatility and robustness of our approach. Across experiments, we show that not only can our method effectively recover the ground-truth parameters but it also performs comparably or better than competing baselines on downstream applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-vo24a, title = {Parameter Estimation in {DAG}s from Incomplete Data via Optimal Transport}, author = {Vo, Vy and Le, Trung and Vuong, Long Tung and Zhao, He and Bonilla, Edwin V. and Phung, Dinh}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {49580--49604}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/vo24a/vo24a.pdf}, url = {https://proceedings.mlr.press/v235/vo24a.html}, abstract = {Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the versatility and robustness of our approach. Across experiments, we show that not only can our method effectively recover the ground-truth parameters but it also performs comparably or better than competing baselines on downstream applications.} }
Endnote
%0 Conference Paper %T Parameter Estimation in DAGs from Incomplete Data via Optimal Transport %A Vy Vo %A Trung Le %A Long Tung Vuong %A He Zhao %A Edwin V. Bonilla %A Dinh Phung %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-vo24a %I PMLR %P 49580--49604 %U https://proceedings.mlr.press/v235/vo24a.html %V 235 %X Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the versatility and robustness of our approach. Across experiments, we show that not only can our method effectively recover the ground-truth parameters but it also performs comparably or better than competing baselines on downstream applications.
APA
Vo, V., Le, T., Vuong, L.T., Zhao, H., Bonilla, E.V. & Phung, D.. (2024). Parameter Estimation in DAGs from Incomplete Data via Optimal Transport. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:49580-49604 Available from https://proceedings.mlr.press/v235/vo24a.html.

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