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Understanding complex predictive models with ghost variables
dc.contributor.author | Delicado Useros, Pedro Francisco |
dc.contributor.author | Peña Sanchez de Rivera, Daniel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa |
dc.date.accessioned | 2023-02-15T13:48:58Z |
dc.date.available | 2023-02-15T13:48:58Z |
dc.date.issued | 2022-08-24 |
dc.identifier.citation | Delicado, P.; Peña, D. Understanding complex predictive models with ghost variables. "Test", 24 Agost 2022, vol. 32; núm. 1; p. 107–145 |
dc.identifier.issn | 1863-8260 |
dc.identifier.uri | http://hdl.handle.net/2117/383386 |
dc.description | The version of record of this article, first published in Test, is available online at Publisher’s website: http://dx.doi.org/10.1007/s11749-022-00826-x |
dc.description.abstract | Framed in the literature on Interpretable Machine Learning, we propose a new procedure to assign a measure of relevance to each explanatory variable in a complex predictive model. We assume that we have a training set to fit the model and a test set to check its out-of-sample performance. We propose to measure the individual relevance of each variable by comparing the predictions of the model in the test set with those obtained when the variable of interest is substituted (in the test set) by its ghost variable, defined as the prediction of this variable by using the rest of explanatory variables. In linear models it is shown that, on the one hand, the proposed measure gives similar results to leave-one-covariate-out (loco, with a lowest computational cost) and outperforms random permutations, and on the other hand, it is strongly related to the usual F-statistic measuring the significance of a variable. In nonlinear predictive models (as neural networks or random forests) the proposed measure shows the relevance of the variables in an efficient way, as shown by a simulation study comparing ghost variables with other alternative methods (including loco and random permutations, and also knockoff variables and estimated conditional distributions). Finally, we study the joint relevance of the variables by defining the relevance matrix as the covariance matrix of the vectors of effects on predictions when using every ghost variable. Our proposal is illustrated with simulated examples and the analysis of a large real data set. |
dc.language.iso | eng |
dc.publisher | Springer |
dc.rights | Attribution 4.0 International |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica |
dc.subject.lcsh | Mathematical statistics |
dc.subject.other | Explainable artificial intelligence |
dc.subject.other | Estimated conditional distributions |
dc.subject.other | Interpretable machine learning |
dc.subject.other | Knockoffs |
dc.subject.other | Leave-one-covariate-out |
dc.subject.other | Out-of-sample prediction |
dc.subject.other | Partial correlation matrix |
dc.subject.other | Random permutations |
dc.title | Understanding complex predictive models with ghost variables |
dc.type | Article |
dc.subject.lemac | Estadística matemàtica |
dc.contributor.group | Universitat Politècnica de Catalunya. ADBD - Anàlisi de Dades Complexes per a les Decisions Empresarials |
dc.identifier.doi | 10.1007/s11749-022-00826-x |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::62 Statistics::62G Nonparametric inference |
dc.subject.ams | Classificació AMS::68 Computer science::68T Artificial intelligence |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s11749-022-00826-x |
dc.rights.access | Open Access |
local.identifier.drac | 34221675 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88142-P/ES/ESTRECHANDO LA BRECHA ENTRE LA ESTADISTICA Y LA CIENCIA DE DATOS/ |
dc.relation.projectid | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-116294GB-I00/ES/ESTADISTICA AVANZADA Y CIENCIA DE DATOS: INTERPRETANDO MODELOS CAJA-NEGRA Y ANALIZANDO CONJUNTOS DE DATOS GRANDES Y COMPLEJOS/ |
local.citation.author | Delicado, P.; Peña, D. |
local.citation.publicationName | Test |
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