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

By Pakize Taylan, Gerhard-Wilhelm Weber, Amir Beck. 2007

87 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI (2019, neutral): “When compared to other models, these are understandable enough to make users feel conﬁdent on using them for practical applications in ﬁnance [193–195] , environmental studies [196] , geology [197] , healthcare [44] , biology [198,199] and energy [200] .”
Optimization Models for Machine Learning: A Survey (2019, methodology): “In [198] the Generalized Additive Model Selection is introduced to fit sparse GAMs in high dimension with a penalized likelihood approach.”
Parameter Estimation in Stochastic Differential Equations (2011, background): “Indeed, with a suitable and maybe adaptive choice of an upper bound M1 [19, 39, 41] we can write our problem as”