Stability selection enables robust learning of differential equations from limited noisy data
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.
Details
Original language | English |
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Article number | 20210916 |
Number of pages | 25 |
Journal | Proceedings of the Royal Society of London : Series A, Mathematical, physical and engineering sciences |
Volume | 478 |
Issue number | 2262 |
Publication status | Published - Jun 2022 |
Peer-reviewed | Yes |
External IDs
PubMedCentral | PMC9199075 |
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Scopus | 85132361601 |
unpaywall | 10.1098/rspa.2021.0916 |
WOS | 000814371000003 |
Mendeley | 6b1c9678-f6d9-31e0-bafb-031b63248a1a |
ORCID | /0000-0003-4414-4340/work/142252172 |
Keywords
Research priority areas of TU Dresden
DFG Classification of Subject Areas according to Review Boards
- Interactive and Intelligent Systems, Image and Language Processing, Computer Graphics and Visualisation
- Massively Parallel and Data-Intensive Systems
- Bioinformatics and Theoretical Biology
- Statistical Physics, Soft Matter, Biological Physics, Nonlinear Dynamics
- Developmental Biology
- Software Engineering and Programming Languages
- Cell Biology
- Biophysics
- Mathematics
Subject groups, research areas, subject areas according to Destatis
Sustainable Development Goals
ASJC Scopus subject areas
Keywords
- PAR proteins, differential equations, machine learning, sparse regression, stability selection, statistical learning theory