New approaches to regression by generalized additive models and continuous optimization for modern applications in finance, science and technology

• Published in: Optimization Vol. 56; no. 5-6; pp. 675 - 698
• Main Authors: Taylan, P., Weber, G.-W., Beck, A.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01.10.2007; Taylor & Francis LLC
• Subjects: Algorithms; Backfitting (Gauss-Seidel) algorithm; Classification; Clustering; Conic quadratic programming; Continuous optimization; Curvature; Density; Financial mathematics; Generalized additive model; Mathematical models; Mathematics Subject Classifications 2000; Optimization algorithms; Optimization techniques; Penalty methods; Quadratic programming; Regression; Regression analysis; Separation of variables; Statistical learning; Studies; Variation
• ISSN: 0233-1934; 1029-4945; 1026-7662; 1029-4945
• DOI: 10.1080/02331930701618740

Generalized additive models belong to modern techniques from statistical learning, and are applicable in many areas of prediction, e.g. in financial mathematics, computational biology, medicine, chemistry and environmental protection. In these models, the expectation of response is linked to the predictors via a link function. These models are fitted through local scoring algorithm using a scatterplot smoother as building blocks proposed by Hastie and Tibshirani (1987). In this article, we first give a short introduction and review. Then, we present a mathematical modeling by splines based on a new clustering approach for the x, their density, and the variation of output y. We contribute to regression with generalized additive models by bounding (penalizing) second-order terms (curvature) of the splines, leading to a more robust approximation. Previously, in [23], we proposed a refining modification and investigation of the backfitting algorithm, applied to additive models. Then, because of drawbacks of the modified backfitting algorithm, we solve this problem using continuous optimization techniques, which will become an important complementary technology and alternative to the concept of modified backfitting algorithm. In particular, we model and treat the constrained residual sum of squares by the elegant framework of conic quadratic programming. ¶This study was carried out as part of Pakize Taylan's postdoc at METU in the program DOSAP.