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As such, they are highly useful for providing trustworthy interpretations of decision-making in domains where complex and opaque machine learning algorithms are utilized. To guarantee their quality and promote user trust, they need to satisfy the <jats:italic>faithfulness<\/jats:italic> desideratum, when supported by the data distribution. We hereby propose a counterfactual generation algorithm for mixed-feature spaces that prioritizes faithfulness through <jats:italic>k-justification<\/jats:italic>, a novel counterfactual property introduced in this paper. The proposed algorithm employs a graph representation of the search space and provides counterfactuals by solving an integer program. In addition, the algorithm is classifier-agnostic and is not dependent on the order in which the feature space is explored. In our empirical evaluation, we demonstrate that it guarantees k-justification while showing comparable performance to state-of-the-art methods in <jats:italic>feasibility<\/jats:italic>, <jats:italic>sparsity<\/jats:italic>, and <jats:italic>proximity<\/jats:italic>.<\/jats:p>","DOI":"10.1007\/s10994-024-06530-1","type":"journal-article","created":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T17:03:29Z","timestamp":1711472609000},"page":"5731-5771","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Ijuice: integer JUstIfied counterfactual explanations"],"prefix":"10.1007","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5460-2491","authenticated-orcid":false,"given":"Alejandro","family":"Kuratomi","sequence":"first","affiliation":[]},{"given":"Ioanna","family":"Miliou","sequence":"additional","affiliation":[]},{"given":"Zed","family":"Lee","sequence":"additional","affiliation":[]},{"given":"Tony","family":"Lindgren","sequence":"additional","affiliation":[]},{"given":"Panagiotis","family":"Papapetrou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,3,26]]},"reference":[{"key":"6530_CR1","doi-asserted-by":"crossref","unstructured":"Basu, A., Conforti, M., Di\u00a0Summa, M., & Jiang, H. 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