TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

Alexander Tong, Jessie Huang, Guy Wolf, David Van Dijk, Smita Krishnaswamy
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:9526-9536, 2020.

Abstract

It is increasingly common to encounter data in the form of cross-sectional population measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model non-linear paths common in many underlying dynamic systems. We establish a link between continuous normalizing flows and dynamic optimal transport to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present \emph{TrajectoryNet}, which controls the continuous paths taken between distributions. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-tong20a, title = {{T}rajectory{N}et: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics}, author = {Tong, Alexander and Huang, Jessie and Wolf, Guy and Van Dijk, David and Krishnaswamy, Smita}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {9526--9536}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/tong20a/tong20a.pdf}, url = {https://proceedings.mlr.press/v119/tong20a.html}, abstract = {It is increasingly common to encounter data in the form of cross-sectional population measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model non-linear paths common in many underlying dynamic systems. We establish a link between continuous normalizing flows and dynamic optimal transport to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present \emph{TrajectoryNet}, which controls the continuous paths taken between distributions. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.} }
Endnote
%0 Conference Paper %T TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics %A Alexander Tong %A Jessie Huang %A Guy Wolf %A David Van Dijk %A Smita Krishnaswamy %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-tong20a %I PMLR %P 9526--9536 %U https://proceedings.mlr.press/v119/tong20a.html %V 119 %X It is increasingly common to encounter data in the form of cross-sectional population measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model non-linear paths common in many underlying dynamic systems. We establish a link between continuous normalizing flows and dynamic optimal transport to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present \emph{TrajectoryNet}, which controls the continuous paths taken between distributions. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.
APA
Tong, A., Huang, J., Wolf, G., Van Dijk, D. & Krishnaswamy, S.. (2020). TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:9526-9536 Available from https://proceedings.mlr.press/v119/tong20a.html.

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