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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. [ABSTRACT FROM AUTHOR]

In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors. [ABSTRACT FROM AUTHOR]

Climate change is becoming an ever important issue due to the possibility that it may result in extreme weather events such as floods or droughts. Consequently, precipitation forecasting has similarly gained in significance as it is a useful tool in meeting the increasing need for the efficient management of water resources as well as in preventing disasters before they happen. In the literature, there are various statistical and computational methods used for this purpose, including linear and nonlinear regression, kriging, time series models, neural networks, and multivariate adaptive regression splines (MARS). Among them, MARS stands out as the better performing precipitation modeling method. In this article, we used a recently developed method called robust conic mars (RCMARS), based on MARS (also on CMARS), to forecast precipitation owing to its ability to model complex uncertain data. In CMARS, which was developed as a powerful alternative to MARS, the model complexity is penalized in the form of Tikhonov regularization and studied as a conic quadratic programming. In RCMARS, on the other hand, CMARS is refined further by including the existence of uncertainty in the future scenarios and robustifying it with a robust optimization technique. To evaluate the performance of the RCMARS method, it was applied to build a precipitation model constructed as an early warning system for the continental Central Anatolia Region of Turkey, where drought has been a recurrent phenomenon for the last few decades. Furthermore, the performance of the RCMARS precipitation model was also compared to that of MARS and CMARS. The results indicated that RCMARS builds more accurate, precise, and stable precipitation models compared to those of MARS and CMARS. In addition to these advantageous features of the RCMARS precipitation model, it also provided a good fit to the data. As a result, we propose its use in precipitation forecasting for the region studied. [ABSTRACT FROM AUTHOR]

Nowadays, the importance of financial crises and defaults of countries are becoming clear due to the globalization in the economic area and investments. Generalized partial linear model (GPLM) is a combination of two different regression models connecting with the mean of the dependent variable with the help of a link function. It is adequate to high-dimensional, non-normal data sets having the flexibility to reflect all anomalies effectively. The nonlinear patterns are also easily explained by the nonparametric component of the model. In this study, we introduce a newly developed conic GPLM (CGPLM) to predict default probabilities of 45 emerging markets using the contribution of a continuous model CMARS and a discrete model logistic regression. We present its application results on a data set with 13 macroeconomic variables in 25 years’ time. To predict debt crises, CGPLM gives better results than a single CMARS and a single logistic regression. In fact, we have 91.81% and 89.31% accuracy rates, computed according to the correctness of the model output, for training and validation sample, respectively. This improvement in prediction of crises can contribute to new prospects and developments in financial mathematics to make more accurate previsions for investments and to take measures due to coming risks. [ABSTRACT FROM PUBLISHER]