Background: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes (GPs), combined with a parallel tempering scheme, and conducts a comparative evaluation with current state-of-the-art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method.
Methods: Methodology for the recently proposed adaptive gradient matching method using GPs, upon which we build our new method, is provided. Details of a competing method using RKHS are also described here.
Results: We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques.
Conclusions: Our study reveals that for known noise variance, our proposed method based on GPs and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust.
Keywords: Gaussian processes; Gradient matching; Ordinary differential equations; Parallel tempering; Parameter inference; Reproducing kernel Hilbert spaces.