Sensitivity analysis in multilinear probabilistic models

Leonelli, M., Görgen, C. and Smith, J. Q. (2017) Sensitivity analysis in multilinear probabilistic models. Information Sciences, 411, pp. 84-97. (doi: 10.1016/j.ins.2017.05.010)

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Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the impact of a parameter change to the Chan–Darwiche distance. Although not fully recognized, the majority of these results rely heavily on the multilinear structure of atomic probabilities in terms of the conditional probability parameters associated with this type of network. By defining a statistical model through the polynomial expression of its associated defining conditional probabilities, we develop here a unifying approach to sensitivity methods applicable to a large suite of models including extensions of Bayesian networks, for instance context-specific ones. Our algebraic approach enables us to prove that for models whose defining polynomial is multilinear both the Chan–Darwiche distance and any divergence in the family of ϕ-divergences are minimized for a certain class of multi-parameter contemporaneous variations when parameters are proportionally covaried.

Item Type:Articles
Additional Information:M. Leonelli was supported by Capes, C. Görgen was supported by the EPSRC grant EP/L505110/1 whilst J.Q. Smith was partly supported by EPSRC grant EP/K039628/1 and The Alan Turing Institute under EPSRC grant EP/N510129/1.
Glasgow Author(s) Enlighten ID:Leonelli, Dr Manuele
Authors: Leonelli, M., Görgen, C., and Smith, J. Q.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Information Sciences
ISSN (Online):1872-6291
Published Online:10 May 2017
Copyright Holders:Copyright © 2017 Elsevier
First Published:First published in Information Sciences 411:84-97
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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