高斯过程回归方法综述

高斯过程回归是基于贝叶斯理论和统计学习理论发展起来的一种全新机器学习方法，适于处理高维数、小样本和非线性等复杂回归问题。在阐述该方法原理的基础上，分析了其存在的计算量大、噪声必须服从高斯分布等问题，给出了改进方法。与神经网络和支持向量机相比，该方法具有容易实现、超参数自适应获取以及输出具有概率意义等优点，方便与预测控制、自适应控制、贝叶斯滤波等相结合。最后总结了其应用情况并展望了未来发展方向。

Overview of Gaussian process regression

Gaussian process regression(GPR) is a new machine learning method by the context of Bayesian theory and
statistical learning theory. It provides a flexible framework for probabilistic regression and is widely used to solve the
high-dimensional, small-sample or nonlinear regression problems. Its principle is introduced in the function-space view and
several limitations such as computational difficulties for large data sets and restrictive modelling assumptions for complex
data sets are discussed. Several improved approaches for these limitations are summarized. GPR is simple to implement,
flexible to nonparameter infer and self-adaptive to determinate hyperparameters in comparison with neural network and
support vector machines. The attractive feature that GPR models provide Gaussian uncertainty estimates for their predictions
allows them to be seamlessly incorporated into predictive control, adaptive control and Bayesian filtering techniques. Finally,
its applications are given and future research trends are prospected.