A parsimonious, computationally efficient machine learning method for spatial regression

The spatial prediction (interpolation) problem arises in various fields of science and engineering that study spatially distributed variables. In the case of scattered data, filling gaps facilitates understanding of the spatial features, visualization of the observed process, and it is also necessary to obtain fully populated grids of spatially dependent parameters used in partial differential equations. Spatial prediction is highly relevant to many disciplines, such as environmental mapping, risk assessment(Christakos, 2012) and environmental health studies (Christakos and Hristopulos, 2013), subsurface hydrology (Kitanidis, 1997; Rubin, 2003), mining (Goovaerts, 1997), and oil reserves estimation (Hohn, 1988; Hamzehpour and Sahimi, 2006). In addition, remote sensing images often include gaps with missing data (e.g., clouds, snow, heavy precipitation, ground vegetation coverage, etc.) that need to be filled (Rossi et al, 1994). Spatial prediction is also useful in image analysis (Winkler, 2003; Gui and Wei, 2004) and signal processing (Unser and Blu, 2005; Ramani and Unser, 2006) including medical applications (Parrott et al, 1993; Cao and Worsley, 2001).