ArticleJournal of the American Statistical Association2022
Kernel Ordinary Differential Equations.
Article in Journal of the American Statistical Association, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- Measuring Regulatory Network Inheritance in Dividing Yeast Cells Using Ordinary Differential Equations.bioRxiv : the preprint server for biology · 2025Article
- Nonparametric estimation via partial derivatives.Journal of the Royal Statistical Society. Series B, Statistical methodology · 2025Article
- MODELING TRAJECTORIES USING FUNCTIONAL LINEAR DIFFERENTIAL EQUATIONS.The annals of applied statistics · 2024Article
- Learning nonparametric ordinary differential equations from noisy data.Journal of computational physics · 2024Article
- A nonlinear sparse neural ordinary differential equation model for multiple functional processes.The Canadian journal of statistics = Revue canadienne de statistique · 2022Article
- A Joint estimation approach to sparse additive ordinary differential equations.Statistics and computing · 2022Article
Corrections and comments
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Authors and funding
2 authors.
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Abstract
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA as well. We demonstrate the efficacy of our method through numerous ODE examples.
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