Learning Stochastic Behaviour from Aggregate Data

Shaojun Ma, Shu Liu, Hongyuan Zha, Haomin Zhou
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:7258-7267, 2021.

Abstract

Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the identity of individual is unavailable. This is in sharp contrast to learning dynamics with full trajectory data, on which the majority of existing methods are based. We propose a novel method using the weak form of Fokker Planck Equation (FPE) — a partial differential equation — to describe the density evolution of data in a sampled form, which is then combined with Wasserstein generative adversarial network (WGAN) in the training process. In such a sample-based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving the partial differential equation (PDE) FPE. We demonstrate our approach in the context of a series of synthetic and real-world data sets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-ma21c, title = {Learning Stochastic Behaviour from Aggregate Data}, author = {Ma, Shaojun and Liu, Shu and Zha, Hongyuan and Zhou, Haomin}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {7258--7267}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/ma21c/ma21c.pdf}, url = {https://proceedings.mlr.press/v139/ma21c.html}, abstract = {Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the identity of individual is unavailable. This is in sharp contrast to learning dynamics with full trajectory data, on which the majority of existing methods are based. We propose a novel method using the weak form of Fokker Planck Equation (FPE) — a partial differential equation — to describe the density evolution of data in a sampled form, which is then combined with Wasserstein generative adversarial network (WGAN) in the training process. In such a sample-based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving the partial differential equation (PDE) FPE. We demonstrate our approach in the context of a series of synthetic and real-world data sets.} }
Endnote
%0 Conference Paper %T Learning Stochastic Behaviour from Aggregate Data %A Shaojun Ma %A Shu Liu %A Hongyuan Zha %A Haomin Zhou %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-ma21c %I PMLR %P 7258--7267 %U https://proceedings.mlr.press/v139/ma21c.html %V 139 %X Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the identity of individual is unavailable. This is in sharp contrast to learning dynamics with full trajectory data, on which the majority of existing methods are based. We propose a novel method using the weak form of Fokker Planck Equation (FPE) — a partial differential equation — to describe the density evolution of data in a sampled form, which is then combined with Wasserstein generative adversarial network (WGAN) in the training process. In such a sample-based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving the partial differential equation (PDE) FPE. We demonstrate our approach in the context of a series of synthetic and real-world data sets.
APA
Ma, S., Liu, S., Zha, H. & Zhou, H.. (2021). Learning Stochastic Behaviour from Aggregate Data. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:7258-7267 Available from https://proceedings.mlr.press/v139/ma21c.html.

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