{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T07:42:41Z","timestamp":1781163761623,"version":"3.54.1"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,10,7]],"date-time":"2017-10-07T00:00:00Z","timestamp":1507334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Bertschinger, Rauh, Olbrich, Jost, and Ay (Entropy, 2014) have proposed a definition of a decomposition of the mutual information     M I ( X : Y , Z )     into shared, synergistic, and unique information by way of solving a convex optimization problem. In this paper, we discuss the solution of their Convex Program from theoretical and practical points of view.<\/jats:p>","DOI":"10.3390\/e19100530","type":"journal-article","created":{"date-parts":[[2017,10,9]],"date-time":"2017-10-09T11:25:35Z","timestamp":1507548335000},"page":"530","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Bivariate Partial Information Decomposition: The Optimization Perspective"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3581-8262","authenticated-orcid":false,"given":"Abdullah","family":"Makkeh","sequence":"first","affiliation":[{"name":"Institute of Computer Science, University of Tartu, 51014 Tartu, Estonia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dirk","family":"Theis","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Tartu, 51014 Tartu, Estonia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raul","family":"Vicente","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Tartu, 51014 Tartu, Estonia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2161","DOI":"10.3390\/e16042161","article-title":"Quantifying unique information","volume":"16","author":"Bertschinger","year":"2014","journal-title":"Entropy"},{"key":"ref_2","unstructured":"Williams, P.L., and Beer, R.D. 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