Proximal Optimal Transport Modeling of Population Dynamics

Charlotte Bunne, Laetitia Papaxanthos, Andreas Krause, Marco Cuturi
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6511-6528, 2022.

Abstract

We propose a new approach to model the collective dynamics of a population of particles evolving with time. As is often the case in challenging scientific applications, notably single-cell genomics, measuring features for these particles requires destroying them. As a result, the population can only be monitored with periodic snapshots, obtained by sampling a few particles that are sacrificed in exchange for measurements. Given only access to these snapshots, can we reconstruct likely individual trajectories for all other particles? We propose to model these trajectories as collective realizations of a causal Jordan-Kinderlehrer-Otto (JKO) flow of measures: The JKO scheme posits that the new configuration taken by a population at time t+1 is one that trades off an improvement, in the sense that it decreases an energy, while remaining close (in Wasserstein distance) to the previous configuration observed at t. In order to learn such an energy using only snapshots, we propose JKOnet, a neural architecture that computes (in end-to-end differentiable fashion) the JKO flow given a parametric energy and initial configuration of points. We demonstrate the good performance and robustness of the JKOnet fitting procedure, compared to a more direct forward method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-bunne22a, title = { Proximal Optimal Transport Modeling of Population Dynamics }, author = {Bunne, Charlotte and Papaxanthos, Laetitia and Krause, Andreas and Cuturi, Marco}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6511--6528}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/bunne22a/bunne22a.pdf}, url = {https://proceedings.mlr.press/v151/bunne22a.html}, abstract = { We propose a new approach to model the collective dynamics of a population of particles evolving with time. As is often the case in challenging scientific applications, notably single-cell genomics, measuring features for these particles requires destroying them. As a result, the population can only be monitored with periodic snapshots, obtained by sampling a few particles that are sacrificed in exchange for measurements. Given only access to these snapshots, can we reconstruct likely individual trajectories for all other particles? We propose to model these trajectories as collective realizations of a causal Jordan-Kinderlehrer-Otto (JKO) flow of measures: The JKO scheme posits that the new configuration taken by a population at time t+1 is one that trades off an improvement, in the sense that it decreases an energy, while remaining close (in Wasserstein distance) to the previous configuration observed at t. In order to learn such an energy using only snapshots, we propose JKOnet, a neural architecture that computes (in end-to-end differentiable fashion) the JKO flow given a parametric energy and initial configuration of points. We demonstrate the good performance and robustness of the JKOnet fitting procedure, compared to a more direct forward method. } }
Endnote
%0 Conference Paper %T Proximal Optimal Transport Modeling of Population Dynamics %A Charlotte Bunne %A Laetitia Papaxanthos %A Andreas Krause %A Marco Cuturi %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-bunne22a %I PMLR %P 6511--6528 %U https://proceedings.mlr.press/v151/bunne22a.html %V 151 %X We propose a new approach to model the collective dynamics of a population of particles evolving with time. As is often the case in challenging scientific applications, notably single-cell genomics, measuring features for these particles requires destroying them. As a result, the population can only be monitored with periodic snapshots, obtained by sampling a few particles that are sacrificed in exchange for measurements. Given only access to these snapshots, can we reconstruct likely individual trajectories for all other particles? We propose to model these trajectories as collective realizations of a causal Jordan-Kinderlehrer-Otto (JKO) flow of measures: The JKO scheme posits that the new configuration taken by a population at time t+1 is one that trades off an improvement, in the sense that it decreases an energy, while remaining close (in Wasserstein distance) to the previous configuration observed at t. In order to learn such an energy using only snapshots, we propose JKOnet, a neural architecture that computes (in end-to-end differentiable fashion) the JKO flow given a parametric energy and initial configuration of points. We demonstrate the good performance and robustness of the JKOnet fitting procedure, compared to a more direct forward method.
APA
Bunne, C., Papaxanthos, L., Krause, A. & Cuturi, M.. (2022). Proximal Optimal Transport Modeling of Population Dynamics . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6511-6528 Available from https://proceedings.mlr.press/v151/bunne22a.html.

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