High-dimensional model representation

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High-dimensional model representation is a finite expansion for a given multivariable function. The expansion is first described by Sobol as

f(\mathbf{x}) = f_0+
\sum_{i=1}^nf_i(x_i)+
\sum_{i,j=1 \atop i<j}^n
f_{ij}(x_{j},x_{j})+ \cdots +
f_{12\ldots n}(x_1,\ldots,x_n).

The method, used to determine the right hand side functions, is given in Sobol's paper.[1] A review can be found here: High Dimensional Model Representation (HDMR): Concepts and Applications.

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References[edit]

  1. ^ Sobol', I. M. (1993), "Sensitivity estimates for nonlinear mathematical models", Mathematical Modeling and Computational Experiment 1 (4): 407–414 (1995), MR 1335161 .