A general framework for modeling Gaussian process with qualitative and quantitative factors

2026-02-18

AI Summary

This work addresses the challenge of jointly modeling qualitative and quantitative factors within Gaussian process frameworks by proposing a unified approach that maps qualitative factors into a continuous latent space, thereby enabling compatibility with standard kernel functions. The proposed framework naturally incorporates ordinal structures inherent in qualitative variables, offering a coherent interpretation of existing modeling strategies while also introducing novel covariance structures. Model construction and selection are performed through latent-variable Gaussian processes, guided by the Bayesian Information Criterion and leave-one-out cross-validation. Extensive experiments demonstrate the method’s effectiveness and superiority over alternative approaches, highlighting its flexibility and robustness in handling mixed input types.

Technology Category

• Knowledge Representation and Reasoning: Qualitative Reasoning
• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• 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: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Computer experiments involving both qualitative and quantitative (QQ) factors have attracted increasing attention. Gaussian process (GP) models have proven effective in this context by choosing specialized covariance functions for QQ factors. In this work, we extend the latent variable-based GP approach, which maps qualitative factors into a continuous latent space, by establishing a general framework to apply standard kernel functions to continuous latent variables. This approach provides a novel perspective for interpreting some existing GP models for QQ factors and introduces new covariance structures in some situations. The ordinal structure can be incorporated naturally and seamlessly in this framework. Furthermore, the Bayesian information criterion and leave-one-out cross-validation are employed for model selection and model averaging. The performance of the proposed method is comprehensively studied on several examples.

Problem

• Gaussian process
• qualitative factors
• quantitative factors
• computer experiments
• covariance functions

Innovation

• Gaussian process
• qualitative and quantitative factors
• latent variable
• covariance function
• model selection