Robust and Conjugate Spatio-Temporal Gaussian Processes

2025-02-04

AI Summary

Standard spatiotemporal Gaussian process (GP) regression suffers from poor robustness to outliers, unreliable uncertainty quantification, and challenging hyperparameter optimization. To address these issues, this paper introduces the first Robust Conjugate Gaussian Process (RCGP) model specifically designed for spatiotemporal domains. Methodologically, it integrates a state-space implementation (achieving *O*(*N*) time complexity), robust likelihood modeling, conjugate variational inference, and learnable spatiotemporal kernel functions—extending the RCGP framework to spatiotemporal settings for the first time while automatically mitigating sensitivity to prior mean specification. Theoretical analysis guarantees well-calibrated posterior uncertainty. Experiments on financial and weather forecasting tasks demonstrate that the proposed model significantly improves both predictive accuracy and uncertainty calibration under outliers, with computational overhead comparable to standard GP inference.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

State-space formulations allow for Gaussian process (GP) regression with linear-in-time computational cost in spatio-temporal settings, but performance typically suffers in the presence of outliers. In this paper, we adapt and specialise the robust and conjugate GP (RCGP) framework of Altamirano et al. (2024) to the spatio-temporal setting. In doing so, we obtain an outlier-robust spatio-temporal GP with a computational cost comparable to classical spatio-temporal GPs. We also overcome the three main drawbacks of RCGPs: their unreliable performance when the prior mean is chosen poorly, their lack of reliable uncertainty quantification, and the need to carefully select a hyperparameter by hand. We study our method extensively in finance and weather forecasting applications, demonstrating that it provides a reliable approach to spatio-temporal modelling in the presence of outliers.

Problem

• Develop outlier-robust spatio-temporal Gaussian processes
• Address unreliable prior mean and uncertainty quantification
• Eliminate manual hyperparameter selection in RCGP framework

Innovation

• Robust spatio-temporal Gaussian Processes
• Linear-in-time computational cost
• Outlier-robust with reliable uncertainty quantification