高斯过程回归的近似方法及其应用

作为机器学习的一个分支，高斯过程回归在近年来越来越受到重视，在诸多领域得到了广泛的应用；该方法适用于非线性系统的建模，并可以自动在模型的复杂度和建模精度之间进行权衡；但是由于计算复杂度较高，其难以直接被应用于大数据量的学习任务，因此，很多近似方法被发展出来以降低其计算成本；根据是否将训练数据划分为子集，高斯过程回归的近似方法可以被分为全局近似方法和局部近似方法；文章首先阐述了高斯过程回归的理论基础，接下来对全局和局部这两种近似方法进行了分析，然后介绍了其在实际应用中的情况，特别是在软测量和控制领域，最后进行了总结和对其未来研究方向的展望。

Approximation Methods of Gaussian Process Regression and Its Application

As a branch of machine learning, Gaussian process regression (GPR) has received increasing attention in recent years and is widely used in many fields. GPR is used for modeling nonlinear systems and can automatically trade-off between model complexity and accuracy. However, due to its high computational complexity, it is difficult to be directly applied to learning tasks with large data sizes. Therefore, many approximation methods are developed to reduce its computational cost. According to whether the training data is divided into subsets, the approximation methods of GPR can be categorized as global and local approximations. This article first describes the theoretical basis of GPR, analyzes these two approximation methods; Then its applications in practice are introduced, especially in the fields of soft sensing and control; Finally, a summary and a prospect of its future research direction are given.