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

Date

2022-01-01

Author

Özmen, Ayşe
Zinchenko, Yuriy
Weber, Gerhard Wilhelm

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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.

Subject Keywords

Robustness and sensitivity analysis, Cross-polytope uncertainty, Robust optimization, MARS, RMARS, Energy and commodity markets, MODELS, OPTIMIZATION, ROBUSTIFICATION, RCMARS, CMARS, PRICE, MARS, Cross-polytope uncertainty, Energy and commodity markets, MARS, RMARS, Robust optimization, Robustness and sensitivity analysis

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85140088020&origin=inward
https://hdl.handle.net/11511/101688

Journal

Annals of Operations Research

DOI

https://doi.org/10.1007/s10479-022-04993-w

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

A. Özmen, Y. Zinchenko, and G. W. Weber, “Robust multivariate adaptive regression splines under cross-polytope uncertainty: an application in a natural gas market,” Annals of Operations Research, pp. 0–0, 2022, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85140088020&origin=inward.