Learning Large Scale Ordinary Differential Equation Systems
By Frederik Vissing Mikkelsen, Niels Richard Hansen. 2017
12 citations recorded by the source corpus.
Learning large scale nonlinear ordinary differential equation (ODE) systems from data is known to be computationally and statistically challenging. We present a framework together with the adaptive integral matching (AIM) algorithm for learning polynomial or rational ODE systems with a sparse network structure. The framework allows for time course data sampled from multiple environments representing e.g. different interventions or perturbations of the system. The algorithm AIM combines an initial penalised integral matching step with an adapted least squares step based on solving the ODE numerically. The R package episode implements AIM together with several other algorithms and is available from CRAN. It is shown that AIM achieves state-of-the-art network recovery for the in silico phosphoprotein abundance data from the eighth DREAM challenge with an AUROC of 0.74, and it is demonstrated via a range of numerical examples that AIM has good statistical properties while being computationally feasible even for large systems.
Subfields: Cardiology and Cardiovascular Medicine, Molecular Biology, Statistical and Nonlinear Physics
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Citations in the corpus
- Causal Models for Dynamical Systems (2020, background): “[2015], Mikkelsen and Hansen [2017]), most of which combine structure learning, that is, model selection, with a parameter inference step.”
- Identifying Causal Structure in Large-Scale Kinetic Systems (2018, methodology): “Exceptions include the approaches with an `1 type penalty and the AIM method by [Mikkelsen and Hansen, 2017].”