Provably Convergent Schrödinger Bridge with Applications to Probabilistic Time Series Imputation

Yu Chen, Wei Deng, Shikai Fang, Fengpei Li, Nicole Tianjiao Yang, Yikai Zhang, Kashif Rasul, Shandian Zhe, Anderson Schneider, Yuriy Nevmyvaka
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:4485-4513, 2023.

Abstract

The Schrödinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized optimal transport problem, which conducts projections onto every other marginal alternatingly. However, in practice, only approximated projections are accessible and their convergence is not well understood. To fill this gap, we present a first convergence analysis of the Schrödinger bridge algorithm based on approximated projections. As for its practical applications, we apply SBP to probabilistic time series imputation by generating missing values conditioned on observed data. We show that optimizing the transport cost improves the performance and the proposed algorithm achieves the state-of-the-art result in healthcare and environmental data while exhibiting the advantage of exploring both temporal and feature patterns in probabilistic time series imputation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-chen23f, title = {Provably Convergent Schrödinger Bridge with Applications to Probabilistic Time Series Imputation}, author = {Chen, Yu and Deng, Wei and Fang, Shikai and Li, Fengpei and Yang, Nicole Tianjiao and Zhang, Yikai and Rasul, Kashif and Zhe, Shandian and Schneider, Anderson and Nevmyvaka, Yuriy}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {4485--4513}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/chen23f/chen23f.pdf}, url = {https://proceedings.mlr.press/v202/chen23f.html}, abstract = {The Schrödinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized optimal transport problem, which conducts projections onto every other marginal alternatingly. However, in practice, only approximated projections are accessible and their convergence is not well understood. To fill this gap, we present a first convergence analysis of the Schrödinger bridge algorithm based on approximated projections. As for its practical applications, we apply SBP to probabilistic time series imputation by generating missing values conditioned on observed data. We show that optimizing the transport cost improves the performance and the proposed algorithm achieves the state-of-the-art result in healthcare and environmental data while exhibiting the advantage of exploring both temporal and feature patterns in probabilistic time series imputation.} }
Endnote
%0 Conference Paper %T Provably Convergent Schrödinger Bridge with Applications to Probabilistic Time Series Imputation %A Yu Chen %A Wei Deng %A Shikai Fang %A Fengpei Li %A Nicole Tianjiao Yang %A Yikai Zhang %A Kashif Rasul %A Shandian Zhe %A Anderson Schneider %A Yuriy Nevmyvaka %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-chen23f %I PMLR %P 4485--4513 %U https://proceedings.mlr.press/v202/chen23f.html %V 202 %X The Schrödinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized optimal transport problem, which conducts projections onto every other marginal alternatingly. However, in practice, only approximated projections are accessible and their convergence is not well understood. To fill this gap, we present a first convergence analysis of the Schrödinger bridge algorithm based on approximated projections. As for its practical applications, we apply SBP to probabilistic time series imputation by generating missing values conditioned on observed data. We show that optimizing the transport cost improves the performance and the proposed algorithm achieves the state-of-the-art result in healthcare and environmental data while exhibiting the advantage of exploring both temporal and feature patterns in probabilistic time series imputation.
APA
Chen, Y., Deng, W., Fang, S., Li, F., Yang, N.T., Zhang, Y., Rasul, K., Zhe, S., Schneider, A. & Nevmyvaka, Y.. (2023). Provably Convergent Schrödinger Bridge with Applications to Probabilistic Time Series Imputation. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:4485-4513 Available from https://proceedings.mlr.press/v202/chen23f.html.

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