Network Reconstruction From High Dimensional Ordinary Differential Equations

TL;DR

This paper introduces a novel non-parametric method for reconstructing high-dimensional dynamical systems from time-course data, avoiding derivative estimation and improving accuracy in network recovery.

Contribution

The authors propose a new approach that bypasses derivative estimation, enabling consistent network recovery in high-dimensional settings with empirical advantages.

Findings

Method outperforms existing approaches in empirical tests.

Can recover true network structure in high dimensions.

Avoids the challenges of noisy derivative estimation.

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 non-parametrically 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.