期刊
JOURNAL OF MATHEMATICAL CHEMISTRY
卷 50, 期 1, 页码 99-130出版社
SPRINGER
DOI: 10.1007/s10910-011-9898-0
关键词
HDMR; Global sensitivity analysis; D-MORPH regression; Extended bases; Least-squares regression; Orthonormal polynomial
资金
- NSF
- ONR
The High Dimensional Model Representation (HDMR) technique decomposes an n-variate function f (x) into a finite hierarchical expansion of component functions in terms of the input variables x = (x (1), x (2), . . . , x (n) ). The uniqueness of the HDMR component functions is crucial for performing global sensitivity analysis and other applications. When x (1), x (2), . . . , x (n) are independent variables, the HDMR component functions are uniquely defined under a specific so called vanishing condition. A new formulation for the HDMR component functions is presented including cases when x contains correlated variables. Under a relaxed vanishing condition, a general formulation for the component functions is derived providing a unique HDMR decomposition of f (x) for independent and/or correlated variables. The component functions with independent variables are special limiting cases of the general formulation. A novel numerical method is developed to efficiently and accurately determine the component functions. Thus, a unified framework for the HDMR decomposition of an n-variate function f (x) with independent and/or correlated variables is established. A simple three variable model with a correlated normal distribution of the variables is used to illustrate this new treatment.
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