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While this theory applies in many settings, it falls short in important data fusion problems, such as two-sample instrumental variable analysis, settings that integrate data from epidemiological studies with diverse designs, and studies with mismeasured variables supplemented by external validation studies. In this paper we derive a comprehensive theory that, in particular, covers these settings by allowing the integration of sources aligned with conditional distributions that do not correspond to a single factorization of the target distribution. We provide a universal characterization of the influence functions of regular and asymptotically linear estimators and the efficient influence function of a target parameter, irrespective of the parameter of interest or the statistical model for the target distribution, thus paving the way for a unified theory for machine-learning debiased, semiparametric efficient estimation.<\/jats:p>","DOI":"10.1214\/25-aos2609","type":"journal-article","created":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T13:51:14Z","timestamp":1782395474000},"page":"1398-1424","source":"Crossref","is-referenced-by-count":3,"title":["Towards a unified theory for semiparametric data fusion with individual-level data"],"prefix":"10.1214","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3238-3769","authenticated-orcid":false,"given":"Ellen","family":"Graham","sequence":"first","affiliation":[{"name":"Department of Biostatistics, University of Washington"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2106-0953","authenticated-orcid":false,"given":"Marco","family":"Carone","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7272-6832","authenticated-orcid":false,"given":"Andrea","family":"Rotnitzky","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"20","doi-asserted-by":"publisher","unstructured":"Graham, B. 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