The new Robust CMARS (RCMARS) method

Date

2010-01-01

Author

Özmen, Ayse
Weber, Gerhard Wilhelm
Batmaz, İnci

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CMARS is an alternative method to a well-known regression tool MARS from data mining and estimation theory. This method is based on a penalized residual sum of squares (PRSS) for MARS as a Tikhonov regularization problem. It treats this problem by a continuous optimization technique called Conic Quadratic Programming (CQP) which permits us to use the interior point methods. CMARS is particularly powerful in handling complex and heterogeneous data containing fixed variables. In this study, we further improve the CMARS method in such a way that it can model the data which contains uncertainty as well. In fact, generally, data include noise in the output and input variables. Consequently, solutions to the optimization problem may present remarkable sensitivity to perturbations in parameters of the problem. The data uncertainty results in uncertain constraints and objective function. To handle this difficulty, we refine our CMARS algorithm by a robust optimization technique which has been proposed to deal with data uncertainty. In this paper, we present the new developed Robust CMARS (RCMARS) method in theory, and illustrate it with a numerical example. © Izmir University of Economics, Turkey, 2010.

Subject Keywords

CMARS, Conic quadratic programming, Data mining, Data uncertainty, Interior point methods, Regression, Robust optimization, Robustness, Tikhonov regularization

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84859710169&origin=inward
https://hdl.handle.net/11511/106539

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Graduate School of Applied Mathematics, Conference / Seminar