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

Janith Petangoda, Chatura Samarakoon, Phillip Stanley-Marbell, 17 October 2024

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 [1, 2] 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 [3] of an uncertainty-tracking processor architecture captures the nuances of the predictive posterior distribution while being ∼108.80x faster than Monte Carlo simulation.

Cite as:

Petangoda, Janith, Chatura Samarakoon, and Phillip Stanley-Marbell. "Gaussian Process Predictions with Uncertain Inputs Enabled by Uncertainty-Tracking Processor Architectures." In NeurIPS 2024 Workshop Machine Learning with new Compute Paradigms.

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