Properties of the Proximate Parameter Tuning Regularization Algorithm |
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Authors: | Martin Brown Fei He Stephen J Wilkinson |
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Institution: | 1.Control Systems Centre, School of Electrical and Electronic Engineering,The University of Manchester,Manchester,UK;2.Department of Chemical and Process Engineering,University of Sheffield,Sheffield,UK |
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Abstract: | An important aspect of systems biology research is the so-called “reverse engineering” of cellular metabolic dynamics from
measured input-output data. This allows researchers to estimate and validate both the pathway’s structure as well as the kinetic
constants. In this paper, the recently published ‘Proximate Parameter Tuning’ (PPT) method for the identification of biochemical
networks is analysed. In particular, it is shown that the described PPT algorithm is essentially equivalent to a sequential
linear programming implementation of a constrained optimization problem. The corresponding objective function consists of
two parts, the first emphasises the data fitting where a residual 1-norm is used, and the second emphasises the proximity
of the calculated parameters to the specified nominal values, using an ∞-norm. The optimality properties of PPT algorithm
solution as well as its geometric interpretation are analyzed. The concept of optimal parameter locus is applied for the exploration
of the entire family of optimal solutions. An efficient implementation of the parameter locus is also developed. Parallels
are drawn with 1-norm parameter deviation regularization which attempt to fit the data with a minimal number of parameters.
Finally, a small example is used to illustrate all of these properties. |
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Keywords: | |
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