Logarithmic High Dimensional Model Representation

This paper presents a new version of the High Dimensional Model Representation (HDMR) which attempts to approximate a given multivariate function by an expansion starting from a constant term and continuing by adding univariate components and then the terms whose multivariances increase via bivariance, trivariance and so on. HDMR works well as long as the function under consideration behaves, more or less, additive. Factorized High Dimensional Model Representation (FHDMR) was considered as a powerful approach working well when the multivariate function under consideration is mostly multiplicative. The additivity of the function was defined through its HDMR components by introducing additivitiy measurers. FHDMR, unfortunately, disabled us to define efficient multiplicativity measurers. Hence, we develope Logarithmic High Dimensional Model Representation (LHDMR) to this end. It removes several unpleasent incapabilities of FHDMR. Key-Words: Multivariate Approximation, High Dimensional Model Representation, Factorized High Dimensional Model Representation, Additivity Measurers, Multiplicativity Measurers