Principal Component Analysis for High Dimension Stochastic Gaussian Process Model Fitting
Maxime Xuereb, Tianming Huo, Szu Hui Ng · 2019
Stochastic Gaussian Process models are widely used in stochastic simulation metamodeling to predict the response of noisy simulations. Often, many real-world engineering problems are high-dimensional (more than 10 dimensions), and the Gaussian Process models' prediction for such high-dimensional inputs are computationally expensive due to multiple inversions of the covariance matrix. Therefore, the “curse of dimensionality” on these models prevent them from being used in a high-dimensional setting. To overcome this problem, a methodology for high-dimensional stochastic Gaussian Process models' fitting is proposed in this paper. The input data is first projected onto a reduced set of dimensions found by Principal Component Analysis before being used to fit the model. Numerical experiments prove that the method helps significantly in reducing the computation time.