Robust conic quadratic programming – A robustification of CMARS (original) (raw)

Abstract

In our previous works, the complexity of Multivariate Adaptive Regression Splines (MARS), which especially means sensitivity with respect to noise in the data, were penalized in the form of Tikhonov regularization (TR), and studied as a Conic Quadratic Programming (CQP) problem. This led to the new method CMARS; it is more model-based and employs continuous, well-structured convex optimisation which uses Interior Point Methods (IPMs) and their codes such as MOSEK™. CMARS is powerful in overcoming complex and heterogeneous data. However, for MARS and CMARS, data are assumed to contain fixed input variables. In fact, data include noise in both output and input variables. Consequently, optimisation problem's solutions can show a remarkable sensitivity to perturbations in the parameters of the problem. In this study, we generalize the regression problem by including the existence of uncertainty in the future scenarios into CMARS, and robustify it with robust optimisation which deals...

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