Accurate and computational efficient estimation with nonlinear statistical models

With the current growing availability of datasets coming from multiple sources and domains, systems onboard our military assets have an immediate need of being functional in multiple domains, handling large amounts of data, and implementing fast and appropriate analyses for these datasets. However, onboard systems often have very limited computational resources upon which to process these tasks. Generalized additive models (GAMs), which are statistical model that are better able to account for non-linear relationships between independent and dependent variables, have been shown in multiple application areas to yield more accurate estimates than models that only assume linear relationships. GAMs require fitting smooth functions of independent variables, and potentially interactions between two or more independent variables with tensor products, commonly using penalized basis splines (P-splines). However, when trying to make predictions for previously unseen feature vectors and without the benefit of significant computing power and necessary software packages, computing the necessary P-spline basis values in order to make predictions becomes computationally intractable. We show that approximating the smooth functions of a trained GAM with cubic splines yields very good estimates that result in minimal loss of accurate compared to the original trained GAM model while significantly decreasing computational cost. These two benefits have resulted in our method being adopted by a primary contractor handling high-fidelity analyses. We will show our implementation results on simulated and real datasets, discuss our findings, and conclude with remarks on future work.