2017/03/23 by Justin Dragon Bewsher, Bewsher, Justin D., Alessandra Tosi +5 · 1 citation
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Laser-induced spectroscopy and plasma #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.1703.08031
openalex publication_date 2017/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical consideration of higher dimensional problems. We fill the gap in the existing literature by deriving the moments of the arc length for a stationary GP with multiple output dimensions. A new method is used to derive the mean of a one-dimensional GP over a finite interval, by considering the distribution of the arc length integrand. This technique is used to derive an approximate distribution over the arc length of a vector valued GP in ℝn by moment matching the distribution. Numerical simulations confirm our theoretical derivations.