Differential Algebra for Model Comparison

TL;DR

This paper introduces a parameter-free method using differential algebra and Gaussian Process Regression to compare and reject competing models based on noisy time-course data, emphasizing transient information.

Contribution

The novel approach combines differential algebra, GPR, and statistical testing to discriminate models without parameter inference, applicable to biological systems.

Findings

Effective discrimination between biological models

No reliance on parameter estimation

Handles noisy data robustly

Abstract

We present a method for rejecting competing models from noisy time-course data that does not rely on parameter inference. First we characterize ordinary differential equation models in only measurable variables using differential algebra elimination. Next we extract additional information from the given data using Gaussian Process Regression (GPR) and then transform the differential invariants. We develop a test using linear algebra and statistics to reject transformed models with the given data in a parameter-free manner. This algorithm exploits the information about transients that is encoded in the model's structure. We demonstrate the power of this approach by discriminating between different models from mathematical biology.