High-dimensional model representation

High-dimensional model representation is a finite expansion for a given multivariable function. The expansion was first described by Ilya M. Sobol[1] 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. A review can be found here: High Dimensional Model Representation (HDMR): Concepts and Applications.