High-dimensional model representation

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

${\displaystyle f(\mathbf {x} )=f_{0}+\sum _{i=1}^{n}f_{i}(x_{i})+\sum _{i,j=1 \atop i<j}^{n}f_{ij}(x_{i},x_{j})+\cdots +f_{12\ldots n}(x_{1},\ldots ,x_{n}).}$

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.

See also

• Variance-based sensitivity analysis
• Volterra series

References

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