🤖 AI Summary
This study addresses the vulnerability of traditional Gaussian Process Regression (GPR) to outliers caused by Gaussian likelihood assumptions by proposing a Generative Gaussian Process Regression model. By constructing an observation-level contamination generative model and employing a variational generalized expectation-maximization algorithm, this approach enables adaptive identification and suppression of outliers. Experiments on both synthetic and real-world datasets demonstrate that the proposed model achieves predictive accuracy superior to or comparable with existing robust GPR methods while maintaining cubic computational complexity. Consequently, this work effectively balances robustness with computational efficiency, offering a novel paradigm for Bayesian regression in noisy environments.
📝 Abstract
Outliers can substantially distort Gaussian process regression (GPR) due to its conventional Gaussian observation likelihood, leading to inaccurate model learning and prediction. To address this limitation, this article introduces a generative GPR model that captures observation-specific contamination and adaptively mitigates the influence of outliers. Subsequently, a variational generalized expectation-maximization procedure is used to learn the latent variables and GPR model parameters. Experiments on synthetic and real datasets under different contamination settings demonstrate that the proposed method remains competitive with-and in several cases outperforms-robust GPR baselines in prediction accuracy. Moreover, the proposed method shares the cubic computational scaling of the compared GPR methods.