A1311
Title: Errors-in-variables Gaussian processes for mixed-input regression
Authors: Sheng Jiang - The Chinese University of Hong Kong, Shenzhen (China) [presenting]
Penghui Fu - The Chinese University of Hong Kong (China)
Abstract: Mixed-input regression is prevalent in real-world applications. While Gaussian processes (GPs) have long been a fundamental tool for nonparametric regression, specifying an appropriate mixed-input covariance kernel remains challenging and is less well understood than its continuous-input counterpart. An errors-in-variables (EIV) framework is proposed that imputes each qualitative input as a latent continuous variable. This reformulation transforms mixed-input regression into a joint model comprising a continuous-input GP in the latent space and a generative mechanism (e.g., a generalized linear model) for the qualitative inputs. The approach enables flexible, well-established kernel choice while preserving interpretability and is particularly well suited for applications where qualitative inputs serve as inexpensive, noisy proxies for expensive, high-accuracy measurements of underlying physical state. Key contributions include (1) a unified modeling framework that generalizes existing mixed-input GPs, (2) an efficient Metropolis-within-Gibbs sampler for joint posterior inference and latent data imputation providing natural uncertainty quantification, and (3) an optional design modeling strategy to enhance latent data estimation accuracy. The framework seamlessly integrates into downstream tasks, providing natural uncertainty quantification, which is typically absent in mixed-variable Bayesian optimization and computer model calibration.
