Prognozowanie konsumpcji gazu ziemnego z wykorzystaniem odpornej metody MARS
Prediction of natural gas consumption using robust MARS

Gerhard-Wilhelm Weber (Wydział Inżynierii Zarządzania, Politechnika Poznańska)


Multivariate Adaptive Regression Spline (MARS) is a modern methodology of data 
mining, statistical learning and estimation theory that is essential in both 
regression and classification. In recent years, MARS is applied in various areas 
of science, technology, finance, and engineering. It is a form of flexible 
non-parametric regression analysis capable of modeling complex data. There, it 
is supposed that the input data are known exactly and equal to some nominal 
values to construct a model. However, both output and input data include noise 
in real life. 

Solutions to optimization problems may present significant sensitivity to 
perturbations in the parameters of the problem. So, optimization affected by 
parameter uncertainty is a focus of the mathematical programming and a need to 
handle uncertain data when optimization results are combined within real-life 
applications. As a result, in inverse problems of modeling, solutions to the 
optimization problems involved in MARS can represent a remarkable sensitivity 
with respect to perturbations in the parameters which base on the data, and a 
computed solution can be highly infeasible, suboptimal, or both. Under this 
motivation, we have included the existence of uncertainty into MARS and 
robustified it through robust optimization which is proposed to cope with data 
and, hence, parametric uncertainty. We have represented Robust MARS (RMARS) 
under polyhedral uncertainty.

In our previous studies, although we had small data sets for our applications, 
the uncertainty matrices for the input data had a huge size since vertices were 
too many to handle. Consequently, we had no enough computer capacity to solve 
our problems for those uncertainty matrices. To overcome this difficulty, we 
obtained different weak RMARS (WRMARS) models for all sample values 
(observations) applying a combinatorial approach and solved them by using MOSEK 
program. Indeed, we have a trade-off between tractability and robustification. 
In this presentation, we present a more robust model using cross-polytope and 
demonstrate its performance with the application of Natural Gas consumption 
prediction. Applying robustification in MARS, we aim to reduce the estimation 
variance. 


Based on:
[1] Özmen, A., Batmaz, I., and Weber, G.-W. (2014) Precipitation modeling by 
    polyhedral RCMARS and comparison with MARS and CMARS, Environmental Modeling 
	and Assessment 19(82), 425–435.
[2] Özmen, A., Weber, G.-W., Çavuşoğlu, Z., and Defterli, Ö. (2013) The new 
    robust conic GPLM method with an application to finance: Prediction of credit 
    default, Journal of Global Optimization 56(2), 233-249.
[3] Özmen, A., Yilmaz, Y., and Weber, G.-W. (2018) Natural gas consumption 
    forecast with MARS and CMARS models for residential users, Energy Economics 
	70, 357–381.