Robust multivariate adaptive regression splines under cross-polytope uncertainty: an application in a natural gas market

Ayşe Özmen (), Yuriy Zinchenko and Gerhard-Wilhelm Weber
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Ayşe Özmen: METU
Yuriy Zinchenko: University of Calgary
Gerhard-Wilhelm Weber: METU

Annals of Operations Research, 2023, vol. 324, issue 1, No 43, 1337-1367

Abstract: Abstract Currently, the presence of data uncertainty and noise raises critical issues to be handled on both theoretical and computational grounds. Therefore, robustification and robust optimization have gained attention from theoretical and practical points of view for the establishment of a modeling framework in mathematical optimization to immunize solutions against diverse uncertainties. Data of both the input and output variables, underlying the problems to be addressed, are affected by the noise of different kinds, such that standard statistical models alone may not be sufficient to ensure trustworthy results due to the complexity of the model. Consequently, we propose including parametric uncertainties reflecting future scenarios in multivariate adaptive regression splines (MARS), which, in turn, show great promise for fitting nonlinear multivariate functions, where additive and interactive effects of the predictors are employed to assess the response variable. We robustify MARS through the usage of robust optimization techniques. Due to the large complexity of the underlying model in prior studies, we applied a so-called weak robustification. Now, we exploit a geometrical and combinatorial approach to allow for a more complete robustification, by formulating Robust MARS (RMARS) under Cross-Polytope Uncertainty. In this study, we use RMARS for energy data and demonstrate its superior performance through a simulation study.

Keywords: Robustness and sensitivity analysis; Cross-polytope uncertainty; Robust optimization; MARS; RMARS; Energy and commodity markets (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10479-022-04993-w

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