Inferring Parsimonious Coupling Statistics in Nonlinear Dynamics with Variational Gaussian Processes

03/08/2022
by   Ameer Ghouse, et al.
0

Nonparametetric methods of uncovering coupling provides a flexible framework for researchers to study network configurations and discover causal graphs. For example, Gaussian Processes have been applied to discover coupling in dynamical systems under the convergent cross-mapping (GP-CCM) framework. Though GP-CCM is a nonparametric method, a function of the data, variations in hyperparameters may impact model results. Maximum marginal likelihood is commonly used to optimize such hyperparameters, however only point estimates are provided from such a routine. In this work, we determine a posteriori the hyperparameter distribution conditioned on the data by the use of variational Bayesian methods with mean field approximations on the posterior distribution of the hyperparameters, thus introducing the variational form of Gaussian process convergent cross-mapping (VGP-CCM). We show that using the a posteriori best approximate model that maximizes evidence of the data for hyperparameters sampling in VGP-CCM, in conjunction with a permutation sampling for the null distribution of uncoupled time series, permits significance statistics that are more robust than mere permutation sampling of the null GP-CCM distribution. We perform tests on synthetic data derived from unidirectionally coupled Lorenz-Rossler systems to demonstrate that the proposed method yields substantially improved specificity over the original GP-CCM.

READ FULL TEXT
research
11/03/2017

Structured Variational Inference for Coupled Gaussian Processes

Sparse variational approximations allow for principled and scalable infe...
research
06/07/2023

Improving Hyperparameter Learning under Approximate Inference in Gaussian Process Models

Approximate inference in Gaussian process (GP) models with non-conjugate...
research
09/17/2023

Double Normalizing Flows: Flexible Bayesian Gaussian Process ODEs Learning

Recently, Gaussian processes have been utilized to model the vector fiel...
research
10/21/2016

Mean-Field Variational Inference for Gradient Matching with Gaussian Processes

Gradient matching with Gaussian processes is a promising tool for learni...
research
11/20/2022

Approximate Uncertainty Propagation for Continuous Gaussian Process Dynamical Systems

When learning continuous dynamical systems with Gaussian Processes, comp...
research
01/14/2020

Robust Gaussian Process Regression with a Bias Model

This paper presents a new approach to a robust Gaussian process (GP) reg...
research
05/19/2017

Streaming Sparse Gaussian Process Approximations

Sparse pseudo-point approximations for Gaussian process (GP) models prov...

Please sign up or login with your details

Forgot password? Click here to reset