Identifying Causal Structure in Large-Scale Kinetic Systems

by   Niklas Pfister, et al.

In the natural sciences, differential equations are widely used to describe dynamical systems. The discovery and verification of such models from data has become a fundamental challenge of science today. From a statistical point of view, we distinguish two problems: parameter estimation and structure search. In parameter estimation, we start from a given differential equation and estimate the parameters from noisy data that are observed at discrete time points. The estimate depends nonlinearly on the parameters. This poses both statistical and computational challenges and makes the task of structure search even more ambitious. Existing methods use either standard model selection techniques or various types of sparsity enforcing regularization, hence focusing on predictive performance. In this work, we develop novel methodology for structure search in ordinary differential equation models. Exploiting ideas from causal inference, we propose to rank models not only by their predictive performance, but also by taking into account stability, i.e., their ability to predict well in different experimental settings. Based on this model ranking we also construct a ranking of individual variables reflecting causal importance. It provides researchers with a list of promising candidate variables that may be investigated further in interventional experiments. Our ranking methodology (both for models and variables) comes with theoretical asymptotic guarantees and is shown to outperform current state-of-the art methods based on extensive experimental evaluation on simulated data. Practical applicability of the procedure is illustrated on a not yet published biological data set. Our methodology is fully implemented. Code will be provided online and will also be made available as an R package.


page 23

page 26

page 28

page 29

page 31


Parameter estimation and model selection for stochastic differential equations for biological growth

In this paper, we consider stochastic versions of three classical growth...

Dynamical Modeling for non-Gaussian Data with High-dimensional Sparse Ordinary Differential Equations

Ordinary differential equations (ODE) have been widely used for modeling...

A regularization method for the parameter estimation problem in ordinary differential equations via discrete optimal control theory

We present a parameter estimation method in Ordinary Differential Equati...

pyPESTO: A modular and scalable tool for parameter estimation for dynamic models

Mechanistic models are important tools to describe and understand biolog...

Reproducing kernel Hilbert space based estimation of systems of ordinary differential equations

Non-linear systems of differential equations have attracted the interest...

Laplace-aided variational inference for differential equation models

Ordinary differential equation (ODE) model whose regression curves are a...

Model Visualization in understanding rapid growth of a journal in an emerging area

A recent independent study resulted in a ranking system which ranked Ast...

Please sign up or login with your details

Forgot password? Click here to reset