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We present techniques to measure the similarity of distributions of data in the federated model. We define sketches for this task that allow efficient estimation of the difference between two distributions based on the total variation distance (\n            <jats:italic toggle=\"yes\">L<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            ) metric. These have accuracy and privacy guarantees, and can be computed incrementally over dynamic data. Our experimental study shows that these are practical to implement and provide accurate estimates.\n          <\/jats:p>","DOI":"10.14778\/3742728.3742736","type":"journal-article","created":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T13:32:53Z","timestamp":1756906373000},"page":"2399-2412","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Federated Data Distribution Shift Estimation"],"prefix":"10.14778","volume":"18","author":[{"given":"Graham","family":"Cormode","sequence":"first","affiliation":[{"name":"Meta and University of Warwick"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Ting","sequence":"additional","affiliation":[{"name":"Meta"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,9,3]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Deep Learning with Differential Privacy. 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