High-dimensional model representation is a finite expansion for a given multivariable function. The expansion was first described by Ilya M. Sobol in his paper "Sensitivity Estimates for Nonlinear Mathematical Models" as

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.

representing the contribution only if all variable act together.

HDMR as an Approximation

The hierarchical representation model of HDMR brings an advantage if one needs to replace an existing model with a simpler one usually containing only univariate or bivariate terms. If the target model does not contain higher level of variable interactions, this approach can yield good approximations with the additional advantage of providing a clearer view of variable interactions.

See also

• Variance-based sensitivity analysis

• Volterra series

References