Spline regression models for complex multi-modal regulatory networks

Ozmen, A.
Kropat, E.
Weber, Gerhard Wilhelm
Complex regulatory networks often have to be further expanded and improved with regard to the unknown effects of additional parameters and factors that can emit a disturbing influence on the key variables under consideration. The concept of target-environment (TE) networks provides a holistic framework for the analysis of such parameter-dependent multi-modal systems. In this study, we consider time-discrete TE regulatory systems with spline entries. We introduce a new regression model for these particular two-modal systems that allows us to determine the unknown system parameters by applying the multivariate adaptive regression spline (MARS) technique and the newly developed conic multivariate adaptive regression spline (CMARS) method. We obtain a relaxation by means of continuous optimization, especially, conic quadratic programming (CQP) that could be conducted by interior point methods. Finally, a numerical example demonstrates the efficiency of the spline-based approach.


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As data become heterogeneous, multiple kernel learning methods may help to classify them. To overcome the drawback lying in its (multiple) finite choice, we propose a novel method of 'infinite' kernel combinations for learning problems with the help of infinite and semi-infinite optimizations. Looking at all the infinitesimally fine convex combinations of the kernels from an infinite kernel set, the margin is maximized subject to an infinite number of constraints with a compact index set and an additional (...
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In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effec...
Existence and stability of almost-periodic solutions of quasi-linear differential equations with deviating argument
Akhmet, Marat (Elsevier BV, 2004-10-01)
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INAN, K (Springer Science and Business Media LLC, 1992-01-01)
Supervisory control problems are formulated in terms of a process model where the mechanism of control is expressed in terms of an algebraic operator with the plant and supervision processes as its arguments. The solution subspaces for supervisory processes restrict the observation and the control capability of supervision. The main result corresponds to decentralized marked supervision under partial observations, and specific cases are derived from this result in a unified, algebraic way. The result and it...
Citation Formats
A. Ozmen, E. Kropat, and G. W. Weber, “Spline regression models for complex multi-modal regulatory networks,” OPTIMIZATION METHODS & SOFTWARE, pp. 515–534, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/50901.