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.

高斯过程已被证明是在给定一组已知训练点的情况下重建函数的强大而灵活的工具，可应用于机器学习、优化和数据同化。然而，当重建的函数具有非平稳或各向异性性质时，它们可能会受到限制。深度高斯过程使用分层过程构建，其中高斯过程的输入本身就是高斯过程，旨在为函数重建提供更灵活的方法。我们根据已知训练点的数量来研究这些深度高斯过程的收敛率。我们还表明，在重建非平稳和各向异性函数时，深度高斯过程回归比标准高斯过程回归取得了更好的结果。