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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]

The multivariate adaptive regression splines (MARS) model is a flexible non-parametric sparse regression algorithm and provides an excellent promise to data fitting through nonlinear basis functions. During the last decades, it is employed in many fields of control design, finance, technology, and science. It can be regarded as an extension of linear models that automatically model interactions and nonlinearities. The least absolute shrinkage and selection operator (LASSO) analysis is a variable selection and shrinkage method to linear regression models. It proposes to construct the subset of explanatory variables which minimizes estimation error to a quantitative dependent variable. LASSO is applied to choose the variables and perform the regularization to improve the interpretability and robustness of the model. In this paper, we examine MARS and LASSO to generate natural gas demand forecasts of residential users for the distribution system operators who need both short- and long-term forecasts. We also compare the performance of MARS and LASSO with a simple multiple-linear regression (LR) commonly used in practice. Our analysis reveals that MARS outperforms LASSO and LR in both the average measures and in the worst-case analysis. For 1 day-ahead forecast, MARS provides a MAPE of around 4.8% while the same figure under LASSO and LR reaches 8.3 and 8.5% respectively. However, as the forecasting horizon increases, we observe that the performance of these proposed methods gets worse and for 1 year-ahead forecast, the MAPE values for MARS, LASSO, and LR are 13.4%, 24.8% and 26.3% respectively. [ABSTRACT FROM AUTHOR]

Residential customers are the main users generally need a great quantity of natural gas in distribution systems, especially, in the wintry weather season since it is particularly consumed for cooking and space heating. Hence, it ought to be noninterruptible. Since distribution systems have a restricted ability for supply, reasonable planning and prediction through the whole year, especially in winter seasons, have emerged as vital. The Ridge Regression (RR) is formulated mainly to decrease collinearity results through shrinking the regression coefficients and reducing the impact in the model of variables. Conic multivariate adaptive regression splines ((C)MARS) model is constructed as an effective choice for MARS by using inverse problems, statistical learning, and multi-objective optimization theories. In this approach, the model complexity is penalized in the structure of RR and it is constructed a relaxation by utilizing continuous optimization, called Conic Quadratic Programming (CQP). In this study, CMARS and RR are applied to obtain forecasts of residential natural gas demand for local distribution companies (LDCs) that require short-term forecasts, and the model performances are compared by using some criteria. Here, our analysis shows that CMARS models outperform RR models. For one-day-ahead forecasts, CMARS yields a MAPE of about 4.8%, while the same value under RR reaches 8.5%. As the forecast horizon increases, it can be seen that the performance of the methods becomes worse, and for a forecast one week ahead, the MAPE values for CMARS and RR are 9.9% and 18.3%, respectively. [ABSTRACT FROM AUTHOR]

Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on several empirical phenomena regarding the behaviour of individual investors, such as how their emotions and opinions influence their decisions. All those emotions and opinions are described by the word Sentiment. In finance, stochastic changes might occur according to investors' sentiment levels. In our study, we aim to represent the mutual effects between some financial process and investors' sentiment with constructing a coupled system of non-autonomous SDEs, evolving in time. These equations are hard to assess and solve. Therefore, we express them in a simplified manner by discretization and Multivariate Adaptive Regression Splines (MARS) model. MARS is a strong method for flexible regression and classification with interactive variables. Hereby, we treat time as another spatial variable. Eventually, we present a modern application with real-world data. This study finishes with a conclusion and an outlook towards future studies. [ABSTRACT FROM AUTHOR]

In financial markets with high uncertainties, the trade-off between maximizing expected return and minimizing the risk is one of the main challenges in modeling and decision making. Since investors mostly shape their invested amounts towards certain assets and their risk aversion level according to their returns, scientists and practitioners have done studies on that subject since the beginning of the stock markets' establishment. In this study, we model a Robust Optimization problem based on data. We found a robust optimal solution to our portfolio optimization problem. This approach includes the use of Robust Conditional Value-at-Risk under Parallelepiped Uncertainty, an evaluation and a numerical finding of the robust optimal portfolio allocation. Then, we trace back our robust linear programming model to the Standard Form of a Linear Programming model; consequently, we solve it by a well-chosen algorithm and software package. Uncertainty in parameters, based on uncertainty in the prices, and a risk-return analysis are crucial parts of this study. A numerical experiment and a comparison (back testing) application are presented, containing real-world data from stock markets as well as a simulation study. Our approach increases the stability of portfolio allocation and reduces the portfolio risk. [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]

Spatial technologies offer high flexibility to handle substantial amount of spatial data and wide range of modelling capabilities. Remotely sensed data are the most significant data source used in spatial technologies. However, it is often associated with uncertainties due to atmospheric effects (i.e. absorption and scattering by atmospheric gases and aerosols). Methods based on rigorous treatment of radiative transfer models still have some drawbacks in the inversion of top of atmospheric reflectance values to surface reflectance values on large numbers of satellite images. In this paper, our aim is to represent a more flexible (adaptive) approach for the regional atmospheric correction by employing nonparametric regression splines within the frame of inverse problems and modern techniques of continuous optimization. To achieve this objective, atmospheric correction models obtained through conic multivariate adaptive regression splines, which is an alternative method to multivariate adaptive regression splines by constructing a penalized residual sum of squares as a Tikhonov regularization problem, are applied on a set of satellite images in order to convert the top of atmospheric reflectance values into surface reflectance values. The results are compared with the ones obtained by both multivariate adaptive regression splines and a radiative transfer-based method. [ABSTRACT FROM PUBLISHER]

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]

This paper contributes to classification and identification in modern finance through advanced optimization. In the last few decades, financial misalignments and, thereby, financial crises have been increasing in numbers due to the rearrangement of the financial world. In this study, as one of the most remarkable of these, countries' debt crises, which result from illiquidity, are tried to predict with some macroeconomic variables. The methodology consists of a combination of two predictive regression models, logistic regression and robust conic multivariate adaptive regression splines (RCMARS), as linear and nonlinear parts of a generalized partial linear model. RCMARS has an advantage of coping with the noise in both input and output data and of obtaining more consistent optimization results than CMARS. An advanced version of conic generalized partial linear model which includes robustification of the data set is introduced: robust conic generalized partial linear model (RCGPLM). This new model is applied on a data set that belongs to 45 emerging markets with 1,019 observations between the years 1980 and 2005. [ABSTRACT FROM AUTHOR]

In order to investigate an association between alcohol consumption and lysosomal cysteine protease induced pancreatic injury and preventive effect of gallic acid as dose-dependent, we determined myeloperoxidase and malondialdehyde levels, serum amylase activities and cathepsin B and L activities in the cytosolic and lysosomal fractions of pancreatic tissue in the ethanol (8 g/kg) and ethanol plus gallic acid (at different doses 50, 100 and 200 mg/kg) given rats. Absolute ethanol (8 g/kg) was given by oral gavage. Gallic acid was dissolved in the saline (2 ml/kg) and administered before 30 min the oral administration of ethanol. Pancreatic myeloperoxidase and also malondialdehyde levels and serum amylase activities were measured. Besides, histological investigations were made. Cathepsin B activities in the cytosolic fraction were decreased by gallic acid (200 mg/kg) and increased in ethanol given rats. Cytosolic/lysosomal ratio of cathepsin B and L were found to be low in the all doses of gallic acid as compared to ethanol group. Serum amylase, pancreatic myeloperoxidase activities and malondialdehyde levels in the ethanol group were higher than in the control group. These were not statistically significant for myeloperoxidase and malondialdehyde. Also, our histopathologic results indicated that ethanol administration increased pancreatic tissue injury. Gallic acid especially at 200 mg/kg improved ethanol-mediated pancreatic tissue damage.In conclusion, gallic acid treatments were decreased release of lysosomal cathepsin B and L enzymes into cytoplasmic fraction and prevented alcohol mediated pancreatic tissue injury. Preventive effect of gallic acid might be dose-dependent. [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]