A graph-theoretic framework for algorithmic design of experiments
A graph-theoretic framework for algorithmic design of experiments
In this paper, we demonstrate that considering experiments in a graph-theoretic manner allows us to exploit automorphisms of the graph to reduce the number of evaluations of candidate designs for those experiments, and thus find optimal designs faster. We show that the use of automorphisms for reducing the number of evaluations required of an optimality criterion function is effective on designs where experimental units have a network structure. Moreover, we show that we can take block designs with no apparent network structure, such as one-way blocked experiments, row-column experiments, and crossover designs, and add
block nodes to induce a network structure. Considering automorphisms can thus reduce the amount of time it takes to find optimal designs for a wide class of experiments.
Linear Network Effects Model, Optimal Design of Experiments, Automorphisms, Block Designs, Isomophic Designs
Parker, Benjamin
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Gilmour, Steven
984dbefa-893b-444d-9aa2-5953cd1c8b03
Koutra, Vasiliki
380da498-0288-4644-86c5-fb8ab984ec6b
Parker, Benjamin
26c5a5ab-17b3-4d6c-ae11-abf3a2554529
Gilmour, Steven
984dbefa-893b-444d-9aa2-5953cd1c8b03
Koutra, Vasiliki
380da498-0288-4644-86c5-fb8ab984ec6b
Parker, Benjamin, Gilmour, Steven and Koutra, Vasiliki
(2018)
A graph-theoretic framework for algorithmic design of experiments
19pp.
Record type:
Monograph
(Working Paper)
Abstract
In this paper, we demonstrate that considering experiments in a graph-theoretic manner allows us to exploit automorphisms of the graph to reduce the number of evaluations of candidate designs for those experiments, and thus find optimal designs faster. We show that the use of automorphisms for reducing the number of evaluations required of an optimality criterion function is effective on designs where experimental units have a network structure. Moreover, we show that we can take block designs with no apparent network structure, such as one-way blocked experiments, row-column experiments, and crossover designs, and add
block nodes to induce a network structure. Considering automorphisms can thus reduce the amount of time it takes to find optimal designs for a wide class of experiments.
Text
NewDesignFrameworkv5-arxiv
- Author's Original
More information
Submitted date: 31 December 2017
e-pub ahead of print date: 28 February 2018
Keywords:
Linear Network Effects Model, Optimal Design of Experiments, Automorphisms, Block Designs, Isomophic Designs
Identifiers
Local EPrints ID: 418434
URI: http://eprints.soton.ac.uk/id/eprint/418434
PURE UUID: 03760deb-ea84-4e20-bf9f-b81d233b46d2
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Date deposited: 08 Mar 2018 17:30
Last modified: 15 Mar 2024 23:12
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Contributors
Author:
Benjamin Parker
Author:
Steven Gilmour
Author:
Vasiliki Koutra
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