Sparse recovery of Diffusion Dynamics: Handling High-Dimensionality in Repeated Short Trajectories

Elise Bayraktar, Charlotte Dion-Blanc
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:469-490, 2026.

Abstract

High-dimensional stochastic differential equations encode complex interaction structures within their drift component. We propose a novel approach to estimate this drift from independent high-frequency trajectory data observed over a short time horizon. Each trajectory is modelled as the solution of a Brownian-driven stochastic differential equation, while the number of time points within each path tends to infinity. We further assume that the drift function governing the dynamics can be expressed as a linear combination of a growing number of Lipschitz basis functions. To promote accurate recovery of the underlying dynamics under sparsity constraints, we propose a Lasso-regularised likelihood criterion. Under suitable regularity conditions, we establish convergence rates for the resulting estimator and emphasise how they depend on the dimensional parameters of the problem, in particular on the number of observed trajectories. We assess the performance of the estimator on synthetic datasets, both from an estimation and a generative perspective. Finally, we illustrate the practical relevance of the approach on a real-world climate dataset, highlighting its ability to perform variable selection.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-bayraktar26a, title = {Sparse recovery of Diffusion Dynamics: Handling High-Dimensionality in Repeated Short Trajectories}, author = {Bayraktar, Elise and Dion-Blanc, Charlotte}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {469--490}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/bayraktar26a/bayraktar26a.pdf}, url = {https://proceedings.mlr.press/v337/bayraktar26a.html}, abstract = {High-dimensional stochastic differential equations encode complex interaction structures within their drift component. We propose a novel approach to estimate this drift from independent high-frequency trajectory data observed over a short time horizon. Each trajectory is modelled as the solution of a Brownian-driven stochastic differential equation, while the number of time points within each path tends to infinity. We further assume that the drift function governing the dynamics can be expressed as a linear combination of a growing number of Lipschitz basis functions. To promote accurate recovery of the underlying dynamics under sparsity constraints, we propose a Lasso-regularised likelihood criterion. Under suitable regularity conditions, we establish convergence rates for the resulting estimator and emphasise how they depend on the dimensional parameters of the problem, in particular on the number of observed trajectories. We assess the performance of the estimator on synthetic datasets, both from an estimation and a generative perspective. Finally, we illustrate the practical relevance of the approach on a real-world climate dataset, highlighting its ability to perform variable selection.} }
Endnote
%0 Conference Paper %T Sparse recovery of Diffusion Dynamics: Handling High-Dimensionality in Repeated Short Trajectories %A Elise Bayraktar %A Charlotte Dion-Blanc %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-bayraktar26a %I PMLR %P 469--490 %U https://proceedings.mlr.press/v337/bayraktar26a.html %V 337 %X High-dimensional stochastic differential equations encode complex interaction structures within their drift component. We propose a novel approach to estimate this drift from independent high-frequency trajectory data observed over a short time horizon. Each trajectory is modelled as the solution of a Brownian-driven stochastic differential equation, while the number of time points within each path tends to infinity. We further assume that the drift function governing the dynamics can be expressed as a linear combination of a growing number of Lipschitz basis functions. To promote accurate recovery of the underlying dynamics under sparsity constraints, we propose a Lasso-regularised likelihood criterion. Under suitable regularity conditions, we establish convergence rates for the resulting estimator and emphasise how they depend on the dimensional parameters of the problem, in particular on the number of observed trajectories. We assess the performance of the estimator on synthetic datasets, both from an estimation and a generative perspective. Finally, we illustrate the practical relevance of the approach on a real-world climate dataset, highlighting its ability to perform variable selection.
APA
Bayraktar, E. & Dion-Blanc, C.. (2026). Sparse recovery of Diffusion Dynamics: Handling High-Dimensionality in Repeated Short Trajectories. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:469-490 Available from https://proceedings.mlr.press/v337/bayraktar26a.html.

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