Abstract: A treatment model that is a first neural network is trained to optimize a treatment loss function based on a treatment variable t using a plurality of observation vectors by regressing t on x(1),z. The trained treatment model is executed to compute an estimated treatment variable value {circumflex over (t)}i for each observation vector. An outcome model that is a second neural network is trained to optimize an outcome loss function by regressing y on x(2) and an estimated treatment variable t. The trained outcome model is executed to compute an estimated first unknown function value {circumflex over (?)}(xi(2)) and an estimated second unknown function value {circumflex over (?)}(xi(2)) for each observation vector. An influence function value is computed for a parameter of interest using {circumflex over (?)}(xi(2)) and {circumflex over (?)}(xi(2)). A value is computed for the predefined parameter of interest using the computed influence function value.

Abstract: A computing device selects a trained spatial regression model. A spatial weights matrix defined for observation vectors is selected, where each element of the spatial weights matrix indicates an amount of influence between respective pairs of observation vectors. Each observation vector is spatially referenced. A spatial regression model is selected from spatial regression models, initialized, and trained using the observation vectors and the spatial weights matrix to fit a response variable using regressor variables. Each observation vector includes a response value for the response variable and a regressor value for each regressor variable of the regressor variables. A fit criterion value is computed for the spatial regression model and the spatial regression model selection, initialization, and training are repeated until each spatial regression model is selected. A best spatial regression model is selected and output as the spatial regression model having an extremum value of the fit criterion value.