Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 478, Issue 2262, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2021.0916
Keywords
statistical learning theory; sparse regression; differential equations; stability selection; PAR proteins; machine learning
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This study presents a robust statistical learning framework for identifying differential equations from noisy spatio-temporal data. The proposed stability-based model selection approach improves robustness against noise by determining the appropriate level of regularization. The combination of stability selection and sparsity-promoting regression methods provides an interpretable criterion and outperforms previous approaches in terms of accuracy, data requirements, and robustness.
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.
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