Network Reconstruction From High-Dimensional Ordinary Differential Equations
By Shizhe Chen, Ali Shojaie, Daniela M. Witten. 2016
81 citations recorded by the source corpus.
ABSTRACT We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.
Subfields: Control and Systems Engineering, Molecular Biology, Statistical and Nonlinear Physics
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
- Niklas Pfister
- Stefan Bauer
- Jan Peters
- Niels Richard Hansen
- Frederik Vissing Mikkelsen
- Sergey Levine
- Pieter Abbeel
- Gerhard Neumann
In Molecular Biology
- Stefan Bauer
- Niklas Pfister
- Jan Peters
- Niels Richard Hansen
- Frederik Vissing Mikkelsen
- Christina Heinze-Deml
- Nicolai Meinshausen
In Statistical and Nonlinear Physics
Citations in the corpus
- Identifying Causal Structure in Large-Scale Kinetic Systems (2018, methodology): “This problem is often formulated as a nonlinear least squares problem argmin θ L∑ `=1 ( X̃t` −Xt` )2 , (2) whose exact solution is often considered as a “gold standard” [e.g., Chen et al., 2017].”
- Learning Large Scale Ordinary Differential Equation Systems (2017, methodology): “In the Lotka-Volterra example it was, for instance, demonstrated that AIM was far superior to GRADE (Chen et al. 2016). This is perhaps unsurprising given that GRADE assumes an additive form of f , but we emphasise this to argue that additivity is a quite strong assumption, which is unlikely to hold”