Transformation and Additivity in Gaussian Processes
Transformation and Additivity in Gaussian Processes
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DOI：
10.1080/00401706.2019.1665592
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发表时间：
2020-10
期刊：
影响因子：
2.5
通讯作者：
Li-Hsiang Lin;V. R. Joseph
中科院分区：
文献类型：
--
作者：
Li-Hsiang Lin;V. R. Joseph
摘要讨论了用高斯过程逼近确定性函数的问题。转换在GP建模中的作用还没有得到很好的理解。我们认为，转换的响应可以用于使确定性函数近似添加剂，然后可以很容易地估计使用添加剂GP。我们称这样的GP为变换加性高斯（TAG）过程。为了捕捉加性模型中未考虑的可能的相互作用，我们提出了一个TAG过程的扩展，称为变换近似加性高斯（TAAG）过程。我们开发了有效的技术来拟合TAAG过程。事实上，我们证明了它可以比标准GP更有效地拟合高维数据。此外，我们表明，使用TAAG过程导致更好的估计，解释，可视化和预测。所提出的方法在R包TAG中实现。
Abstract We discuss the problem of approximating a deterministic function using Gaussian processes (GPs). The role of transformation in GP modeling is not well understood. We argue that transformation of the response can be used for making the deterministic function approximately additive, which can then be easily estimated using an additive GP. We call such a GP a transformed additive Gaussian (TAG) process. To capture possible interactions which are unaccounted for in an additive model, we propose an extension of the TAG process called transformed approximately additive Gaussian (TAAG) process. We develop efficient techniques for fitting a TAAG process. In fact, we show that it can be fitted to high-dimensional data much more efficiently than a standard GP. Furthermore, we show that the use of the TAAG process leads to better estimation, interpretation, visualization, and prediction. The proposed methods are implemented in the R package TAG.