Learning and Transferring Geographically Weighted Regression Trees across Time

Abstract

The Geographically Weighted Regression (GWR) is a method of spatial statistical analysis which allows the exploration of geographical differences in the linear effect of one or more predictor variables upon a response variable. The parameters of this linear regression model are locally determined for every point of the space by processing a sample of distance decay weighted neighboring observations. While this use of locally linear regression has proved appealing in the area of spatial econometrics, it also presents some limitations. First, the form of the GWR regression surface is globally defined over the whole sample space, although the parameters of the surface are locally estimated for every space point. Second, the GWR estimation is founded on the assumption that all predictor variables are equally relevant in the regression surface, without dealing with spatially localized collinearity problems. Third, time dependence among observations taken at consecutive time points is not considered as information-bearing for future predictions. In this paper, a tree-structured approach is adapted to recover the functional form of a GWR model only at the local level. A stepwise approach is employed to determine the local form of each GWR model by selecting only the most promising predictors. Parameters of these predictors are estimated at every point of the local area. Finally, a time-space transfer technique is tailored to capitalize on the time dimension of GWR trees learned in the past and to adapt them towards the present. Experiments confirm that the tree-based construction of GWR models improves both the local estimation of parameters of GWR and the global estimation of parameters performed by classical model trees. Furthermore, the effectiveness of the time-space transfer technique is investigated.