Physics Inspired Approaches To Understanding Gaussian Processes
This work offers incremental insights for researchers and practitioners using Gaussian Processes by enhancing interpretability and performance in applications.
The paper tackled the problem of understanding the decision-making process of Gaussian Process models by analyzing their loss landscape using physics-inspired methods, demonstrating that typical hyperparameter values for Matern kernels are suboptimal and providing practical guidance to improve performance and interpretability.
Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this work, we contribute an analysis of the loss landscape for GP models using methods from physics. We demonstrate $ν$-continuity for Matern kernels and outline aspects of catastrophe theory at critical points in the loss landscape. By directly including $ν$ in the hyperparameter optimisation for Matern kernels, we find that typical values of $ν$ are far from optimal in terms of performance, yet prevail in the literature due to the increased computational speed. We also provide an a priori method for evaluating the effect of GP ensembles and discuss various voting approaches based on physical properties of the loss landscape. The utility of these approaches is demonstrated for various synthetic and real datasets. Our findings provide an enhanced understanding of the decision-making process behind GPs and offer practical guidance for improving their performance and interpretability in a range of applications.