On ANOVA expansions and strategies for choosing the anchor point
On ANOVA expansions and strategies for choosing the anchor point
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DOI：
10.1016/j.amc.2010.08.061
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发表时间：
2010-12
期刊：
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通讯作者：
Zhen Gao;J. Hesthaven
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文献类型：
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作者：
Zhen Gao;J. Hesthaven
经典的Lebesgue ANOVA展开提供了一种优雅的方式来表示依赖于高维参数集的函数，并且一旦构造了ANOVA表示，它通常可以大幅降低此类函数的评估成本。不幸的是，由于需要计算高维积分，展开式本身的构造是昂贵的。解决这个问题的一种方法是考虑另一种公式，称为锚定ANOVA扩展。该公式不需要积分，但具有敏感地依赖于被称为锚点的特殊参数的选择的精度。我们提出了一个比较研究的几种策略选择这个锚点，并认为这个锚点的最佳选择是一个稀疏的网格求积的中心点。这种选择不会导致额外的成本，并且正如我们将展示的那样，会导致ANOVA展开的自然截断。的效率和准确性说明通过几个标准的基准，这种选择被证明优于替代品在一系列的应用。
The classic Lebesgue ANOVA expansion offers an elegant way to represent functions that depend on a high-dimensional set of parameters and it often enables a substantial reduction in the evaluation cost of such functions once the ANOVA representation is constructed. Unfortunately, the construction of the expansion itself is expensive due to the need to evaluate high-dimensional integrals. A way around this is to consider an alternative formulation, known as the anchored ANOVA expansion. This formulation requires no integrals but has an accuracy that depends sensitively on the choice of a special parameter, known as the anchor point. We present a comparative study of several strategies for the choice of this anchor point and argue that the optimal choice of this anchor point is the center point of a sparse grid quadrature. This choice induces no additional cost and, as we shall show, results in a natural truncation of the ANOVA expansion. The efficiency and accuracy is illustrated through several standard benchmarks and this choice is shown to outperform the alternatives over a range of applications.