RMARS: Robustification of multivariate adaptive regression spline under polyhedral uncertainty

- By the robust optimization technique we refine the regression and classification method MARS.
- Related to this, we involve the existence of uncertainty in this data mining tool.
- We present Robust MARS (RMARS) in theory and method.
- We show that models from RMARS have much less variability in parameter estimates.
- We also show that models from RMARS have less variability in accuracy measures.

Since, with increased volatility and further uncertainties, financial crises translated a high “noise” within data from financial markets and economies into the related models, recent years' events in the financial world have led to radically untrustworthy representations of the future. Hence, robustification started to attract more attention in finance. The presence of noise and data uncertainty raises critical problems to be dealt with on the theoretical and computational side. For immunizing against parametric uncertainties, robust optimization has gained greatly in importance as a modeling framework from both a theoretical and a practical point of view. Consequently, we include the existence of uncertainty considering future scenarios in the multivariate adaptive regression spline (MARS) that has an apparent success in modeling real-life data in a variety of application fields, and robustify it through robust optimization proposed to cope with data and resulting model parameter uncertainty. We represent the new Robust MARS (RMARS) in theory and method and apply RMARS on financial market data. We demonstrate its good performance with a simulation study and a numerical experience that refers to basic economic indicators. Results indicate that models from RMARS have much less variability in parameter estimates and in accuracy measures, to the cost of just a slightly lower accuracy than MARS.