Locally induced Gaussian processes for large-scale simulation experiments
Locally induced Gaussian processes for large-scale simulation experiments
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DOI：
10.1007/s11222-021-10007-9
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发表时间：
2020-08
影响因子：
2.2
通讯作者：
D. Cole;R. Christianson;R. Gramacy
中科院分区：
文献类型：
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作者：
D. Cole;R. Christianson;R. Gramacy
高斯过程（GP）作为复杂表面的灵活替代品，但在大训练数据大小的矩阵分解的立方成本下会出现问题。地理空间和机器学习社区建议使用伪输入或诱导点作为一种策略，以获得近似值，从而减轻计算负担。然而，我们展示了如何放置的诱导点和他们的众多可以阻挠病理，特别是在大规模的动态响应面建模任务。作为补救措施，我们建议移植诱导点的想法，这通常是全球性的，到一个更本地的情况下，选择是更容易和更快。通过这种方式，我们提出的方法混合了全局诱导点和基于数据子集的局部GP逼近。提供了一个级联的战略规划选择的本地诱导点，并比较绘制相关的方法，重点是计算机代理建模应用。我们表明，当地的诱导点扩展其全球和数据子集的准确性计算效率的前沿组成部分。基准数据和大规模的真实模拟卫星阻力插值问题提供了说明性的例子。
Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or inducing points, as one strategy to obtain an approximation easing that computational burden. However, we show how placement of inducing points and their multitude can be thwarted by pathologies, especially in large-scale dynamic response surface modeling tasks. As remedy, we suggest porting the inducing point idea, which is usually applied globally, over to a more local context where selection is both easier and faster. In this way, our proposed methodology hybridizes global inducing point and data subset-based local GP approximation. A cascade of strategies for planning the selection of local inducing points is provided, and comparisons are drawn to related methodology with emphasis on computer surrogate modeling applications. We show that local inducing points extend their global and data subset component parts on the accuracy–computational efficiency frontier. Illustrative examples are provided on benchmark data and a large-scale real-simulation satellite drag interpolation problem.