Active Learning via Heteroskedastic Rational Kriging

2025-07-14

AI Summary

To address low sampling efficiency in surrogate modeling of complex computer simulations, this paper identifies a key limitation of conventional stationary Gaussian process (GP) active learning: when the response surface exhibits weak local variations, it tends to disperse design points excessively, leading to inefficient resource utilization. We propose an active learning method based on heteroscedastic rational kernel Kriging (HRKK), the first to integrate a heteroscedastic GP framework with a rational quadratic kernel to accurately capture spatial non-stationarity in functional variation intensity. HRKK maintains or improves predictive accuracy while achieving 10–100× faster computation than state-of-the-art non-stationary GP methods. Extensive evaluations—including multiple synthetic benchmarks and two real-world datasets—demonstrate significant improvements in both surrogate model accuracy and sampling efficiency in critical regions.

Technology Category

• Machine Learning: Active Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Active learning methods for emulating complex computer models that rely on stationary Gaussian processes tend to produce design points that uniformly fill the entire experimental region, which can be wasteful for functions which vary only in small regions. In this article, we propose a new Gaussian process model that captures the heteroskedasticity of the function. Active learning using this new model can place design points in the more interesting regions of the response surface, and thus obtain surrogate models with better accuracy. The proposed active learning method is compared with the state-of-the-art methods using simulations and two real datasets. It is found to have comparable or better performance relative to other non-stationary Gaussian process-based methods, but faster by orders of magnitude.

Problem

• Improves active learning for non-uniform functions
• Addresses inefficiency in stationary Gaussian processes
• Enhances surrogate model accuracy and speed

Innovation

• Heteroskedastic Gaussian process model
• Targeted active learning placement
• Faster non-stationary performance