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GridEx: An Algorithm for Knowledge Extraction from Black-Box Regressors

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Abstract

Knowledge-extraction methods are applied to ML-based predictors to attain explainable representations of their operation when the lack of interpretable results constitutes a problem. Several algorithms have been proposed for knowledge extraction, mostly focusing on the extraction of either lists or trees of rules. Yet, most of them only support supervised learning – and, in particular, classification – tasks. Iter is among the few rule-extraction methods capable of extracting symbolic rules out of sub-symbolic regressors. However, its performance – here intended as the interpretability of the rules it extracts – easily degrades as the complexity of the regression task at hand increases.

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Building creditrisk evaluation expert systems using neural network rule extraction and decision tables
  • B Baesens
  • R Setiono
  • V De Lille
  • S Viaene
  • J Vanthienen
Baesens, B., Setiono, R., De Lille, V., Viaene, S., Vanthienen, J.: Building creditrisk evaluation expert systems using neural network rule extraction and decision tables. In: ICIS 2001 Proceedings, vol. 20 (2001). http://aisel.aisnet.org/icis2001/ 20
Interpretable narrative explanation for ML predictors with LP: a case study for XAI
  • R Calegari
  • G Ciatto
  • J Dellaluce
  • A Omicini
Calegari, R., Ciatto, G., Dellaluce, J., Omicini, A.: Interpretable narrative explanation for ML predictors with LP: a case study for XAI. In: Bergenti, F., Monica, S. (eds.) WOA 2019-20th Workshop "From Objects to Agents", CEUR Workshop Proceedings, vol. 2404, pp. 105-112. Sun SITE Central Europe, RWTH Aachen University, 26-28 June 2019. http://ceur-ws.org/Vol-2404/paper16.pdf
  • J R Quinlan
Quinlan, J.R.: C4.5: Programming for Machine Learning. Morgan Kauffmann 38, 48 (1993)