{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,18]],"date-time":"2022-06-18T00:13:02Z","timestamp":1655511182668},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"\n \n We study the marginal-MAP problem on graphical models, and present a novel approximation method based on direct approximation of the sum operation. A primary difficulty of marginal-MAP problems lies in the non-commutativity of the sum and max operations, so that even in highly structured models, marginalization may produce a densely connected graph over the variables to be maximized, resulting in an intractable potential function with exponential size. We propose a chain decomposition approach for summing over the marginalized variables, in which we produce a structured approximation to the MAP component of the problem consisting of only pairwise potentials. We show that this approach is equivalent to the maximization of a specific variational free energy, and it provides an upper bound of the optimal probability. Finally, experimental results demonstrate that our method performs favorably compared to previous methods.\n \n <\/jats:p>","DOI":"10.1609\/aaai.v26i1.8394","type":"journal-article","created":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T20:23:31Z","timestamp":1654115011000},"page":"1882-1887","source":"Crossref","is-referenced-by-count":0,"title":["Approximating the Sum Operation for Marginal-MAP Inference"],"prefix":"10.1609","volume":"26","author":[{"given":"Qiang","family":"Cheng","sequence":"first","affiliation":[]},{"given":"Feng","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Jianwu","family":"Dong","sequence":"additional","affiliation":[]},{"given":"Wenli","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"Ihler","sequence":"additional","affiliation":[]}],"member":"9382","published-online":{"date-parts":[[2021,9,20]]},"container-title":["Proceedings of the AAAI Conference on Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/8394\/8253","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/8394\/8253","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T23:57:19Z","timestamp":1655510239000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/8394"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,7,26]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v26i1.8394","relation":{},"ISSN":["2374-3468","2159-5399"],"issn-type":[{"value":"2374-3468","type":"electronic"},{"value":"2159-5399","type":"print"}],"subject":[],"published":{"date-parts":[[2021,9,20]]}}}