Bayesian generative kernel Gaussian process regression

The Bayesian generative kernel Gaussian process regression (BGKGPR), a novel progressive probabilistic approach for nonparametric modeling with an optimal generative kernel, is proposed. In Gaussian process (GP) regression, a kernel is assigned to represent the similarity between the input data. Conventional kernels are assigned as the commonly used kernels with all input variables, and a trial-and-error procedure is applied to obtain the finalized kernel. However, an improper choice of the kernel type and/or redundant input variables can significantly degrade the modeling performance. To address this problem, the proposed approach provides a generative kernel augmentation scheme to develop the optimal kernel with the appropriate input variables. The scheme starts with a candidate kernel set. By adopting more features, these candidates evolve as augmented kernels. A Bayesian indicator is formulated to assess the performance of the potential kernels. Hence, the set of kernels that strike the optimal balance between fitting capacity and robustness is chosen for further enhancement. The generation procedure is conducted iteratively until further augmentation ceases to provide considerable improvement in the kernel performance. The proposed approach has three appealing features. First, the optimal kernel with the appropriate input variables can be generated. Second, the resultant kernel can be obtained efficiently in an automatic manner. Third, the uncertainty of all estimates can be quantified. To illustrate the efficacy of the proposed approach, two numerical examples and a case study with three-year continuous monitoring of a 22-story reinforced concrete building are presented.