Inferring Parsimonious Coupling Statistics in Nonlinear Dynamics with Variational Gaussian Processes

Falsification is the basis for testing existing hypotheses, and a great danger is posed when results incorrectly reject our prior notions (false positives). Though nonparametric and nonlinear exploratory methods of uncovering coupling provide a flexible framework to study network configurations and discover causal graphs, multiple comparisons analyses make false positives more likely, exacerbating the need for their control. We aim to robustify the Gaussian Processes Convergent Cross-Mapping (GP-CCM) method through Variational Bayesian Gaussian Process modeling (VGP-CCM). We alleviate computational costs of integrating with conditional hyperparameter distributions through mean field approximations. This approximation model, in conjunction with permutation sampling of the null distribution, permits significance statistics that are more robust than permutation sampling with point hyperparameters. Simulated unidirectional Lorenz-Rossler systems as well as mechanistic models of neurovascular systems are used to evaluate the method. The results demonstrate that the proposed method yields improved specificity, showing promise to combat false positives.