This introduction aims to provide readers an intuitive understanding of Gaussian processes regression. Gaussian processes regression (GPR) models have been widely used in machine learning applications because their representation flexibility and inherently uncertainty measures over predictions. The paper starts with explaining mathematical basics that Gaussian processes built on including multivariate normal distribution, kernels, non-parametric models, joint and conditional probability. The Gaussian processes regression is then described in an accessible way by balancing showing unnecessary mathematical derivation steps and missing key conclusive results. An illustrative implementation of a standard Gaussian processes regression algorithm is provided. Beyond the standard Gaussian processes regression, existing software packages to implement state-of-the-art Gaussian processes algorithms are reviewed. Lastly, more advanced Gaussian processes regression models are specified. The paper is written in an accessible way, thus undergraduate science and engineering background will find no difficulties in following the content.

中文翻译：

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高斯过程回归的直观教程

本介绍旨在让读者对高斯过程回归有一个直观的了解。高斯过程回归 (GPR) 模型已广泛用于机器学习应用中，因为它们的表示灵活性和固有的对预测的不确定性度量。本文首先解释了高斯过程建立的数学基础，包括多元正态分布、核、非参数模型、联合和条件概率。然后通过平衡显示不必要的数学推导步骤和丢失的关键结论性结果，以一种易于理解的方式描述高斯过程回归。提供了标准高斯过程回归算法的说明性实现。除了标准的高斯过程回归，审查了实现最先进的高斯过程算法的现有软件包。最后，指定了更高级的高斯过程回归模型。论文以通俗易懂的方式撰写，因此本科理工科背景在遵循内容方面不会有任何困难。