Feasible Point Algorithms with Applications in Parametric and Kernel-Based Shape-Constrained Regression
Buch, Englisch, 194 Seiten, Format (B × H): 148 mm x 210 mm
ISBN: 978-3-8396-2097-7
Verlag: Fraunhofer Verlag
Shape-constrained regression enhances traditional regression by incorporating prior knowledge through shape constraints like monotonicity and convexity. These constraints, often derived from physical laws, are beneficial in engineering fields where data is limited and noisy.
This thesis examines two optimization problems: shape-constrained parametric ridge regression and shape-constrained kernel ridge regression. By rigorously enforcing various shape constraints, these problems become convex semi-infinite optimization problems. To computationally tackle these problems, two adaptive discretization algorithms - the Core Algorithm and the Composite Algorithm - are developed. These efficiently compute approximate feasible solutions within finite iterations while controlling optimality errors. The research covers parametric regression with polynomial and posynomial models, and kernel methods using Gaussian kernels. Real-world manufacturing case studies demonstrate the practicality of these methods. This work advances the theory of shape-constrained regression and provides algorithms to compute interpretable predictive models in small data settings where shape knowledge is given.
This thesis examines two optimization problems: shape-constrained parametric ridge regression and shape-constrained kernel ridge regression. By rigorously enforcing various shape constraints, these problems become convex semi-infinite optimization problems. To computationally tackle these problems, two adaptive discretization algorithms - the Core Algorithm and the Composite Algorithm - are developed. These efficiently compute approximate feasible solutions within finite iterations while controlling optimality errors. The research covers parametric regression with polynomial and posynomial models, and kernel methods using Gaussian kernels. Real-world manufacturing case studies demonstrate the practicality of these methods. This work advances the theory of shape-constrained regression and provides algorithms to compute interpretable predictive models in small data settings where shape knowledge is given.
Poursanidis / Fraunhofer ITWM
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Fachgebiete
- Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik Industrielle Qualitätskontrolle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
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