{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T18:53:43Z","timestamp":1757616823817,"version":"3.44.0"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T00:00:00Z","timestamp":1718236800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T00:00:00Z","timestamp":1718236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","award":["16KISA050K"],"award-info":[{"award-number":["16KISA050K"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["MO 3877\/1-1"],"award-info":[{"award-number":["MO 3877\/1-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005711","name":"Universit\u00e4t Hamburg","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005711","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["K\u00fcnstl Intell"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Privacy-preserving inference aims to avoid revealing identifying information about individuals during inference. Lifted probabilistic inference works with groups of indistinguishable individuals, which has the potential to prevent tracing back a query result to a particular individual in a group. Therefore, we investigate how lifting, by providing anonymity, can help preserve privacy in probabilistic inference. Specifically, we show correspondences between <jats:italic>k<\/jats:italic>-anonymity and lifting and present <jats:italic>s-symmetry<\/jats:italic> as an analogue as well as PAULI, a privacy-preserving inference algorithm that ensures s-symmetry during query answering.<\/jats:p>","DOI":"10.1007\/s13218-024-00851-y","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T23:39:08Z","timestamp":1718235548000},"page":"225-241","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Lifting in Support of Privacy-Preserving Probabilistic Inference"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9056-7673","authenticated-orcid":false,"given":"Marcel","family":"Gehrke","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0911-2582","authenticated-orcid":false,"given":"Johannes","family":"Liebenow","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2799-8128","authenticated-orcid":false,"given":"Esfandiar","family":"Mohammadi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0282-4284","authenticated-orcid":false,"given":"Tanya","family":"Braun","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,13]]},"reference":[{"issue":"3","key":"851_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1798596.1798602","volume":"6","author":"G Aggarwal","year":"2010","unstructured":"Aggarwal G, Panigrahy R, Feder T, Thomas D, Kenthapadi K, Khuller S, Zhu A (2010) Achieving anonymity via clustering. ACM Trans Algor (TALG) 6(3):1\u201319","journal-title":"ACM Trans Algor (TALG)"},{"key":"851_CR2","doi-asserted-by":"crossref","unstructured":"Bayardo RJ, Agrawal R (2005) Data privacy through optimal k-anonymisation. In: ICDE-05 proceedings of the 21st international conference on data engineering, pp 217\u2013228. IEEE","DOI":"10.1109\/ICDE.2005.42"},{"key":"851_CR3","unstructured":"Boyen X, Koller D (1998) Tractable inference for complex stochastic processes. In: Proceedings of the fourteenth conference on uncertainty in artificial intelligence, pp 33\u201342. Morgan Kaufmann Publishers Inc"},{"key":"851_CR4","unstructured":"Braun T (2020) Rescued from a sea of queries: exact inference in probabilistic relational models. Ph.D. thesis, University of L\u00fcbeck"},{"key":"851_CR5","doi-asserted-by":"crossref","unstructured":"Braun T, M\u00f6ller R (2016) Lifted junction tree algorithm. In: Proceedings of KI 2016: advances in artificial intelligence, pp 30\u201342. Springer","DOI":"10.1007\/978-3-319-46073-4_3"},{"key":"851_CR6","doi-asserted-by":"crossref","unstructured":"Braun T, M\u00f6ller R (2018) Parameterised queries and lifted query answering. In: IJCAI-18 Proceedings of the 27th international joint conference on artificial intelligence, pp 4980\u20134986. IJCAI Organization","DOI":"10.24963\/ijcai.2018\/691"},{"key":"851_CR7","unstructured":"Chang A, Ghazi B, Kumar R, Manurangsi P (2021) Locally private k-means in one round. In: International conference on machine learning, pp 1441\u20131451. PMLR"},{"key":"851_CR8","unstructured":"Cohen A(2022) Attacks on deidentification\u2019s defenses. In: USENIX-22 proceedings of the 31st USENIX security symposium, pp 1469\u20131486. USENIX Association"},{"key":"851_CR9","unstructured":"De\u00a0Raedt L, Kimmig A, Toivonen H(2007) ProbLog: a probabilistic prolog and its application in link discovery. In: IJCAI-07 proceedings of 20th international joint conference on artificial intelligence, pp 2062\u20132467. IJCAI Organization"},{"issue":"6","key":"851_CR10","doi-asserted-by":"publisher","first-page":"4744","DOI":"10.1109\/TPWRS.2016.2524678","volume":"31","author":"K Dehghanpour","year":"2016","unstructured":"Dehghanpour K, Nehrir MH, Sheppard JW, Kelly NC (2016) Agent-based modeling in electrical energy markets using dynamic bayesian networks. IEEE Trans Power Syst 31(6):4744\u20134754","journal-title":"IEEE Trans Power Syst"},{"issue":"1","key":"851_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"A Dempster","year":"1977","unstructured":"Dempster A, Laird N, Rubin D (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Statist Soc Seri B Methodol 39(1):1\u201338","journal-title":"J R Statist Soc Seri B Methodol"},{"key":"851_CR12","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s41324-021-00421-6","volume":"30","author":"WMD Dlamini","year":"2021","unstructured":"Dlamini WMD, Simelane SP, Nhlabatsi NM (2021) Bayesian network-based spatial predictive modelling reveals COVID-19 transmission dynamics in Eswatini. Spat Inf Res 30:183\u2013194","journal-title":"Spat Inf Res"},{"key":"851_CR13","doi-asserted-by":"crossref","unstructured":"Dwork C, Kenthapadi K, McSherry F, Mironov I, Naor M (2006) Our data, ourselves: privacy via distributed noise generation. In: Annual international conference on the theory and applications of cryptographic techniques, pp 486\u2013503. Springer","DOI":"10.1007\/11761679_29"},{"issue":"3\u20134","key":"851_CR14","first-page":"211","volume":"9","author":"C Dwork","year":"2014","unstructured":"Dwork C, Roth A et al (2014) The algorithmic foundations of differential privacy. Found Trends Theor Comput Sci 9(3\u20134):211\u2013407","journal-title":"Found Trends Theor Comput Sci"},{"key":"851_CR15","doi-asserted-by":"crossref","unstructured":"Finke N, Mohr M (2021) A priori approximation of symmetries in probabilistic dynamic relational models. In: KI 2021: Advances in artificial intelligence, pp 309\u2013323. Springer","DOI":"10.1007\/978-3-030-87626-5_23"},{"key":"851_CR16","unstructured":"Gehrke M (2021) Taming exact inference in temporal probabilistic relational models. Ph.D. thesis, University of L\u00fcbeck"},{"key":"851_CR17","unstructured":"Gehrke M, Braun T, M\u00f6ller R, Relational forward backward algorithm for multiple queries. In: FLAIRS-32 proceedings of the 32nd international florida artificial intelligence research society conference"},{"key":"851_CR18","doi-asserted-by":"crossref","unstructured":"Gehrke M, Braun T, M\u00f6ller R (2018) Lifted dynamic junction tree algorithm. In: Proceedings of the 23rd international conference on conceptual structures, pp 55\u201369. Springer","DOI":"10.1007\/978-3-319-91379-7_5"},{"key":"851_CR19","doi-asserted-by":"crossref","unstructured":"Gehrke M, Brau, T, M\u00f6ller R (2019) Uncertain evidence for probabilistic relational models. In: Proceedings of the 32nd Canadian conference on artificial intelligence, Canadian AI 2019, pp 80\u201393. Springer","DOI":"10.1007\/978-3-030-18305-9_7"},{"key":"851_CR20","unstructured":"Gehrke M, M\u00f6ller R, Braun T (2020) Taming reasoning in temporal probabilistic relational models. In: ECAI-20 proceedings of the 24th European conference on artificial intelligence, pp. 2592\u20132599"},{"key":"851_CR21","unstructured":"Gogate V, Domingos PM (2011) Probabilistic theorem proving. In: UAI-11 proceedings of the twenty-seventh conference on uncertainty in artificial intelligence, pp. 256\u2013265. AUAI Press"},{"key":"851_CR22","doi-asserted-by":"crossref","unstructured":"Hartwig M, Braun T, M\u00f6ller R (2021) Handling overlaps when lifting gaussian bayesian networks. In: IJCAI-21 proceedings of the 30th international joint conference on artificial intelligence, pp. 4980\u20134986. IJCAI Organization","DOI":"10.24963\/ijcai.2021\/581"},{"key":"851_CR23","doi-asserted-by":"crossref","unstructured":"Hossain NUI, Shah C (2023) Dynamic bayesian network based approach for modeling and assessing resilience of smart grid system. In: Handbook of smart energy systems, pp. 1613\u20131632. Springer (2023)","DOI":"10.1007\/978-3-030-97940-9_16"},{"key":"851_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3389\/fpubh.2022.876691","volume":"10","author":"DP Johnson","year":"2022","unstructured":"Johnson DP, Lulla V (2022) Predicting COVID-19 community infection relative risk with a dynamic bayesian network. Front Public Health 10:1\u201324","journal-title":"Front Public Health"},{"key":"851_CR25","doi-asserted-by":"crossref","unstructured":"Jones M, Nguyen HL, Nguyen TD (2021) Differentially private clustering via maximum coverage. AAAI-21 proceedings of the AAAI conference on artificial intelligence, 35(13), 11555\u201311563","DOI":"10.1609\/aaai.v35i13.17375"},{"key":"851_CR26","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1111\/j.2517-6161.1988.tb01721.x","volume":"50","author":"SL Lauritzen","year":"1988","unstructured":"Lauritzen SL, Spiegelhalter DJ (1988) Local computations with probabilities on graphical structures and their application to expert systems. J R Statist Soc Ser B Methodol 50:157\u2013224","journal-title":"J R Statist Soc Ser B Methodol"},{"key":"851_CR27","doi-asserted-by":"crossref","unstructured":"LeFevre K, DeWitt DJ, Ramakrishnan R (2006) Mondrian multidimensional k-anonymity. In: ICDE-06 proceedings of the 22nd international conference on data engineering, pp 25\u201325. IEEE","DOI":"10.1109\/ICDE.2006.101"},{"key":"851_CR28","doi-asserted-by":"crossref","unstructured":"Li J, Wong RCW, Fu AWC, Pei J (2006) Achieving k-anonymity by clustering in attribute hierarchical structures. In: DaWaK-06 proceedings of the 8th international conference on data warehousing and knowledge discovery, pp 405\u2013416. Springer","DOI":"10.1007\/11823728_39"},{"key":"851_CR29","doi-asserted-by":"crossref","unstructured":"Li N, Li T, Venkatasubramanian S (2007) t-Closeness: privacy beyond k-anonymity and l-diversity. In: 2007 IEEE 23rd international conference on data engineering, pp 106\u2013115. IEEE","DOI":"10.1109\/ICDE.2007.367856"},{"key":"851_CR30","doi-asserted-by":"crossref","unstructured":"Luttermann M, Braun T, M\u00f6ller R, Gehrke M (2024) Colour passing revisited: lifted model construction with commutative factors. In: AAAI-24 proceedings of the 38th AAAI conference on artificial intelligence, pp 20500\u201320507. AAAI Press","DOI":"10.1609\/aaai.v38i18.30034"},{"key":"851_CR31","doi-asserted-by":"crossref","unstructured":"Machanavajjhala A, Gehrke J, Kifer D, Venkitasubramaniam M (2006) l-diversity: privacy beyond k-anonymity. In: ICDE-06 proceddings of the 22nd international conference on data engineering","DOI":"10.1109\/ICDE.2006.1"},{"key":"851_CR32","unstructured":"Milch B, Zettlemoyer LS, Kersting K, Haimes M, Kaelbling LP (2008) Lifted probabilistic inference with counting formulas. In: AAAI-08 proceedings of the 23rd national conference on artificial intelligence - volume 2, pp. 1062\u20131068. AAAI Press"},{"key":"851_CR33","unstructured":"Morik K, Rahnenf\u00fchrer J, Wietfeld C (2023) Machine learning under resource constraints. De Gruyter"},{"key":"851_CR34","unstructured":"Murphy KP (2002) Dynamic bayesian networks: representation, inference and learning. Ph.D. thesis, University of California, Berkeley"},{"key":"851_CR35","doi-asserted-by":"crossref","unstructured":"Nguyen HL, Chaturvedi A, Xu EZ (2021) Differentially private k-means via exponential mechanism and max cover. In: Proceedings of the AAAI conference on artificial intelligence, 35, 9101\u20139108 (2021)","DOI":"10.1609\/aaai.v35i10.17099"},{"key":"851_CR36","doi-asserted-by":"crossref","unstructured":"Niepert M, Van\u00a0den Broeck G (2014) Tractability through exchangeability: a new perspective on efficient probabilistic inference. In: AAAI-14 proceedings of the twenty-eighth AAAI conference on artificial intelligence, pp 2467\u20132475. AAAI Press","DOI":"10.1609\/aaai.v28i1.9073"},{"key":"851_CR37","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/s11004-023-10087-5","volume":"56","author":"M Pazo","year":"2024","unstructured":"Pazo M, Boente C, Albuquerque T, Gerassis S, Roque N, Taboada J (2024) Unpacking occupational health data in the service sector: from bayesian networking and spatial clustering to policy-making. Math Geosci 56:465\u2013485. https:\/\/doi.org\/10.1007\/s11004-023-10087-5","journal-title":"Math Geosci"},{"key":"851_CR38","doi-asserted-by":"crossref","unstructured":"Pei J, Xu J, Wang Z, Wang W, Wang K (2007) Maintaining k-anonymity against incremental updates. In: SSDBM-07 proceedings of the 19th international conference on scientific and statistical database management, pp 1\u201312. IEEE","DOI":"10.1109\/SSDBM.2007.16"},{"key":"851_CR39","unstructured":"Poole D (2003) First-order probabilistic inference. In: IJCAI-03 proceedings of the 18th international joint conference on artificial intelligence, pp 985\u2013991. Morgan Kaufmann Publishers Inc"},{"issue":"1","key":"851_CR40","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s10994-006-5833-1","volume":"62","author":"M Richardson","year":"2006","unstructured":"Richardson M, Domingos P (2006) Markov logic networks. Mach Learn 62(1):107\u2013136","journal-title":"Mach Learn"},{"key":"851_CR41","unstructured":"de\u00a0Salvo\u00a0Braz R, Amir E, Roth D (2005) Lifted first-order probabilistic inference. In: IJCAI-05 Proceedings of the 19th international joint conference on artificial intelligence, pp 1319\u20131325. IJCAI Organization"},{"key":"851_CR42","unstructured":"Samarati P, Sweeney L (1998) Protecting privacy when disclosing information: k-anonymity and its enforcement through generalization and suppression"},{"key":"851_CR43","doi-asserted-by":"crossref","unstructured":"Su D, Cao J, Li N, Bertino E, Jin H (2016) Differentially private k-means clustering. In: Proceedings of the 6th ACM conference on data and application security and privacy, pp 26\u201337","DOI":"10.1145\/2857705.2857708"},{"issue":"05","key":"851_CR44","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1142\/S021848850200165X","volume":"10","author":"L Sweeney","year":"2002","unstructured":"Sweeney L (2002) Achieving k-anonymity privacy protection using generalization and suppression. Int J Uncertain Fuzz Knowl Based Syst 10(05):571\u2013588","journal-title":"Int J Uncertain Fuzz Knowl Based Syst"},{"issue":"5","key":"851_CR45","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1142\/S0218488502001648","volume":"10","author":"L Sweeney","year":"2002","unstructured":"Sweeney L (2002) K-anonymity: a model for protecting privacy. Int J Uncertain Fuzz Knowl Based Syst 10(5):557\u2013570","journal-title":"Int J Uncertain Fuzz Knowl Based Syst"},{"key":"851_CR46","unstructured":"Taghipour N, Davis J, Blockeel H (2013) First-order decomposition trees. In: NIPS-13 Proceedings of the 26th international conference on neural information processing systems - 1, 1052\u20131060. Curran Associates Inc"},{"issue":"1","key":"851_CR47","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1613\/jair.3793","volume":"47","author":"N Taghipour","year":"2013","unstructured":"Taghipour N, Fierens D, Davis J, Blockeel H (2013) Lifted variable elimination: decoupling the operators from the constraint language. J Artif Intell Res 47(1):393\u2013439","journal-title":"J Artif Intell Res"},{"key":"851_CR48","doi-asserted-by":"crossref","unstructured":"Treiber A, Molina A, Weinert C, Schneider T, Kersting K (2020) CryptoSPN: privacy-preserving sum-product network inference. In: ECAI-20 proceedings of the 24th European conference on artificial intelligence, pp 1946\u20131953. IOS Press","DOI":"10.3233\/FAIA200313"},{"key":"851_CR49","doi-asserted-by":"crossref","unstructured":"Van\u00a0den Broeck G, Davis J (2012) Conditioning in first-order knowledge compilation and lifted probabilistic inference. In: AAAI-12 proceedings of the twenty-sixth AAAI conference on artificial intelligence, pp 1961\u20131967. AAAI Press","DOI":"10.1609\/aaai.v26i1.8404"},{"key":"851_CR50","unstructured":"Van\u00a0den Broeck G, Taghipour N, Meert W, Davis J, De\u00a0Raedt L (2011) Lifted Probabilistic inference by first-order knowledge compilation. In: IJCAI-11 proceedings of the twenty-second international joint conference on artificial intelligence, pp 2178\u20132185. AAAI Press\/international joint conferences on artificial intelligence"},{"key":"851_CR51","doi-asserted-by":"crossref","unstructured":"Wang Y, van Bremen T, Wang Y, Ku\u017eelka O (2022) Domain-lifted sampling for universal two-variable logic and extensions. In: AAAI-22 proceedings of the 36th AAAI conference on artificial intelligence, pp 10070\u201310079. AAAI Press","DOI":"10.1609\/aaai.v36i9.21246"},{"issue":"4","key":"851_CR52","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3134428","volume":"42","author":"J Zhang","year":"2017","unstructured":"Zhang J, Cormode G, Procopiuc CM, Srivastava D, Xiao X (2017) Privbayes: private data release via bayesian networks. ACM Trans Datab Syst (TODS) 42(4):1\u201341","journal-title":"ACM Trans Datab Syst (TODS)"},{"key":"851_CR53","unstructured":"Zhang NL, Poole D (1994) A simple approach to bayesian network computations. In: Proceedings of the 10th Canadian conference on artificial intelligence, pp 171\u2013178. Springer"},{"key":"851_CR54","doi-asserted-by":"publisher","first-page":"89555","DOI":"10.1109\/ACCESS.2022.3201641","volume":"10","author":"Z Zhou","year":"2022","unstructured":"Zhou Z, Wang Y, Yu X, Miao J (2022) A targeted privacy-preserving data publishing method based on Bayesian network. IEEE Access 10:89555\u201389567","journal-title":"IEEE Access"}],"container-title":["KI - K\u00fcnstliche Intelligenz"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13218-024-00851-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13218-024-00851-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13218-024-00851-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T20:29:00Z","timestamp":1757104140000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13218-024-00851-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,13]]},"references-count":54,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["851"],"URL":"https:\/\/doi.org\/10.1007\/s13218-024-00851-y","relation":{},"ISSN":["0933-1875","1610-1987"],"issn-type":[{"type":"print","value":"0933-1875"},{"type":"electronic","value":"1610-1987"}],"subject":[],"published":{"date-parts":[[2024,6,13]]},"assertion":[{"value":"25 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}