Anisotropy and non-stationarity in statistical learning, and its influence on the convergence of function approximation

统计学习中的各向异性和非平稳性及其对函数逼近收敛性的影响

• 批准号: 2436448
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2436448
• 关键词: Anisotropy; non; stationarity; statistical; learning

Gaussian processes have proved to be a powerful and flexible tool in the reconstruction of functions given a set of known training points, with applications in machine learning, optimisation and data assimilation. However, they can be limited when the functions being reconstructed are of a non-stationary or anisotropic nature. Deep Gaussian processes, constructed using a hierarchical process where the inputs to a Gaussian process are themselves Gaussian processes, aim to give a more flexible approach to function reconstruction. We look at convergence rates of these deep Gaussian processes in terms of the number of known training points. We also show that deep Gaussian process regression achieves considerably better results than standard Gaussian process regression when reconstructing non-stationary and anisotropic functions.

高斯过程在给定一组已知训练点的函数重建中被证明是一个强大而灵活的工具，在机器学习、优化和数据同化中有应用。然而，当重构的函数是非平稳的或各向异性的性质时，它们可能受到限制。深度高斯过程，使用层次过程构造，其中高斯过程的输入本身就是高斯过程，旨在提供更灵活的函数重建方法。我们根据已知训练点的数量来观察这些深度高斯过程的收敛速度。我们还发现深度高斯过程回归在重建非平稳和各向异性函数时取得了比标准高斯过程回归更好的结果。