Spatial Lasso with Applications to GIS Model Selection

Geographic information systems (GIS) organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate layers, but also of choosing appropriate neighborhoods within those layers. We formalize this problem and propose the use of Lasso to simultaneously select variables, choose neighborhoods, and estimate parameters. Spatial smoothness in selected coefficients is incorporated through use of a priori spatial covariance structure, and this leads to a modification of the Lasso procedure. The LARS algorithm, which can be used in a fast implementation of Lasso, is also modified to yield a fast implementation of spatial Lasso. The spatial Lasso performs well in numerical examples, including an application to prediction of soil moisture.