Optimal Kernel Learning for Gaussian Process Models with High-Dimensional Input
This work addresses a domain-specific problem for engineers and scientists using surrogate modeling in simulations, offering an incremental improvement by integrating existing concepts from optimal design and experiment analysis.
The paper tackles the problem of Gaussian process regression struggling with high computational costs and low prediction accuracy in high-dimensional input scenarios by proposing an optimal kernel learning approach to identify active variables, demonstrating improved prediction accuracy and correct identification of active input variables through examples.
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation involves too many input variables. For some simulation models, the outputs may only be significantly influenced by a small subset of the input variables, referred to as the ``active variables''. We propose an optimal kernel learning approach to identify these active variables, thereby overcoming GP model limitations and enhancing system understanding. Our method approximates the original GP model's covariance function through a convex combination of kernel functions, each utilizing low-dimensional subsets of input variables. Inspired by the Fedorov-Wynn algorithm from optimal design literature, we develop an optimal kernel learning algorithm to determine this approximation. We incorporate the effect heredity principle, a concept borrowed from the field of ``design and analysis of experiments'', to ensure sparsity in active variable selection. Through several examples, we demonstrate that the proposed method outperforms alternative approaches in correctly identifying active input variables and improving prediction accuracy. It is an effective solution for interpreting the surrogate GP regression and simplifying the complex underlying system.