Regression analysis for clusters in gene-environment networks based on ellipsoidal calculus and optimization

Date

2010-11-29

Author

Kropat, Erik
Weber, Gerhard Wilhelm
Rüickmann, Jan-J.

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In this paper, we discuss regression models for gene-environment networks under ellipsoidal uncertainty. Functionally related groups of genes and environmental factors are identified by clustering techniques and the corresponding uncertain states are represented in terms of ellipsoids. The timedependent expression values are determined by a regulatory system where the interactions between the clusters are defined by (affine-) linear coupling rules. Ellipsoidal calculus is applied to determine explicit representations of the uncertain multivariate states of the system. Various regression models are introduced for an estimation of the unknown system parameters which depend on uncertain (ellipsoidal) measurement data. Herewith, we offer an Elliptic Operations Research, in which we analyze the structure of the optimization problems obtained, especially, in view of their solvability by semidefinite programming and interior point methods, we discuss the structural frontiers and research challenges, and we conclude with an outlook. Copyright © 2010 Watam Press.

Subject Keywords

Computational biology, Computational statistics, Dynamical systems, Ellipsoidal OR, Exact clustering, Gene-environment networks, Identification, Semidefinite programming, Systems biology, Uncertainty

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=78649304564&origin=inward
https://hdl.handle.net/11511/106883

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Graduate School of Applied Mathematics, Article