Measuring regional effects of model inputs with random Forest

In many disciplines involving high-dimensional data, permutation variable importance measure (PVIM) based on random forest is widely used for importance ranking of model inputs. This work extends the traditional PVIM to investigate the regional effects of the internal value range of model inputs. The PVIM function is firstly defined to measure the residual PVIM when the distribution range of one input variable is reduced to its subranges. An efficient computational algorithm is developed, and clear mathematic meaning for the proposed computational procedure is interpreted. The proposed method is further demonstrated with Ishigami function and a multi-indicator system model.