标题： 一种具有神经网络参数的非平稳高斯过程框架 显示英文标题

标题： A Framework for Nonstationary Gaussian Processes with Neural Network Parameters

摘要： 高斯过程因其灵活性和不确定性量化而成为非参数回归的流行工具。 然而，它们通常使用平稳核，这限制了模型的表达能力，并可能不适合许多数据集。 我们提出了一种框架，使用其参数在特征空间中变化的非平稳核，将这些参数建模为以特征作为输入的神经网络的输出。 神经网络和高斯过程通过链式法则计算导数进行联合训练。 我们的方法清晰地描述了非平稳参数的行为，并与用于扩展到大型数据集的近似方法兼容。 它具有灵活性，并且可以轻松适应不同的非平稳核，而无需重新设计优化过程。 我们的方法使用GPyTorch库实现，可以轻松修改。 我们在几个机器学习数据集上测试了我们方法的非平稳方差和噪声变体，发现其准确性以及对数得分均优于平稳模型和使用变分推理近似的分层模型。 对于仅具有非平稳方差的模型，也观察到了类似的结果。 我们还展示了我们的方法恢复空间数据的非平稳参数的能力。 显示英文摘要

摘要： Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be unsuitable for many datasets. We propose a framework that uses nonstationary kernels whose parameters vary across the feature space, modeling these parameters as the output of a neural network that takes the features as input. The neural network and Gaussian process are trained jointly using the chain rule to calculate derivatives. Our method clearly describes the behavior of the nonstationary parameters and is compatible with approximation methods for scaling to large datasets. It is flexible and easily adapts to different nonstationary kernels without needing to redesign the optimization procedure. Our methods are implemented with the GPyTorch library and can be readily modified. We test a nonstationary variance and noise variant of our method on several machine learning datasets and find that it achieves better accuracy and log-score than both a stationary model and a hierarchical model approximated with variational inference. Similar results are observed for a model with only nonstationary variance. We also demonstrate our approach's ability to recover the nonstationary parameters of a spatial dataset.