Gaussian Process Predictions with Uncertain Inputs Enabled by Uncertainty-Tracking Processor Architectures

Abstract

Gaussian Processes (GPs) are theoretically-grounded models that capture both aleatoric and epistemic uncertainty, but, the well-known solutions of the GP predictive posterior distribution apply only for deterministic inputs. If the input is uncertain, closed-form solutions aren't generally available and approximation schemes such as moment-matching and Monte Carlo simulation must be used. Moment-matching is only available under restricted conditions on the input distribution and the GP prior and will miss the nuances of the predictive posterior distribution; Monte Carlo simulation can be computationally expensive. In this article, we present a _general_ method that uses a recently-developed processor architecture capable of performing arithmetic on distributions to implicitly calculate the predictive posterior distribution with uncertain inputs. We show that our method implemented to run on a commercially-available implementation of an uncertainty-tracking processor architecture captures the nuances of the predictive posterior distribution while being ${\sim}108.80$x faster than Monte Carlo simulation.