不等式约束下高斯过程的高维逼近
Finite-dimensional approximation of Gaussian processes with inequality constraints
摘要：
高斯过程由于其灵活性，在非参数函数估计中得到了广泛的应用。关于底层函数的先验信息通常是可用的。例如，物理系统（计算机模型输出）可能已知满足关于一些或所有输入的不等式约束。我们开发了一个有限维近似的GPS能够将不等式约束和嘈杂的观察计算机模型仿真器。它是基于高斯随机系数和确定性基函数之间的线性组合。通过这种方法，不等式约束在整个域中得到尊重。后验分布的平均值和最大值被很好地定义。仿真研究表明，该模型的效率和性能的预测精度和不确定性量化。
英文摘要：
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all inputs. We develop a finite-dimensional approximation of GPs capable of incorporating inequality constraints and noisy observations for computer model emulators. It is based on a linear combination between Gaussian random coefficients and deterministic basis functions. By this methodology , the inequality constraints are respected in the entire domain. The mean and the maximum of the posterior distribution are well defined. A simulation study to show the efficiency and the performance of the proposed model in term of predictive accuracy and uncertainty quantification is included.
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