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A geometric characterization of sensitivity analysis in monomial models

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dc.contributor.authorLeonelli, Manuele
dc.contributor.authorRiccomagno, Eva
dc.contributor.rorhttps://ror.org/02jjdwm75
dc.date.accessioned2025-04-01T10:23:00Z
dc.date.available2025-04-01T10:23:00Z
dc.date.issued2022-12
dc.description.abstractSensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability at a time and observing how this affects output probabilities of interest. When one probability is varied, then others are proportionally covaried to respect the sum-to-one condition of probabilities. The choice of proportional covariation is justified by multiple optimality conditions, under which the original and the varied distributions are as close as possible under different measures. For variations of more than one parameter at a time and for the large class of discrete statistical models entertaining a regular monomial parametrisation, we demonstrate the optimality of newly defined proportional multi-way schemes with respect to an optimality criterion based on the I-divergence. We demonstrate that there are varying parameters’ choices for which proportional covariation is not optimal and identify the sub-family of distributions where the distance between the original distribution and the one where probabilities are covaried proportionally is minimum. This is shown by adopting a new geometric characterization of sensitivity analysis in monomial models, which include most probabilistic graphical models. We also demonstrate the optimality of proportional covariation for multi-way analyses in Naive Bayes classifiers.
dc.description.peerreviewedyes
dc.description.statusPublished
dc.formatapplication/pdf
dc.identifier.citationLeonelli, M., & Riccomagno, E. (2022). A geometric characterization of sensitivity analysis in monomial models. International Journal of Approximate Reasoning, 151, 64-84. https://doi.org/10.1016/j.ijar.2022.09.006.
dc.identifier.doihttps://doi.org/10.1016/j.ijar.2022.09.006
dc.identifier.issn1873-4731
dc.identifier.urihttps://hdl.handle.net/20.500.14417/3678
dc.journal.titleInternational Journal of Approximate Reasoning
dc.language.isoen
dc.page.final84
dc.page.initial64
dc.page.total21
dc.publisherElsevier
dc.relation.departmentComputer Science & AI
dc.relation.entityIE University
dc.relation.schoolIE School of Science & Technology
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.en
dc.subject.keywordBayesian network classifiers
dc.subject.keywordCovariation
dc.subject.keywordI-projections
dc.subject.keywordMonomial models
dc.subject.keywordSensitivity analysis
dc.titleA geometric characterization of sensitivity analysis in monomial models
dc.typeinfo:eu-repo/semantics/article
dc.version.typeinfo:eu-repo/semantics/publishedVersion
dc.volume.number151
dspace.entity.typePublication
relation.isAuthorOfPublicationbc86b9eb-18b3-4fab-bf14-ad6f5509312f
relation.isAuthorOfPublication.latestForDiscoverybc86b9eb-18b3-4fab-bf14-ad6f5509312f
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