{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T15:29:02Z","timestamp":1780500542838,"version":"3.54.1"},"reference-count":7,"publisher":"MIT Press - Journals","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2000,1,1]]},"abstract":"<jats:p> Graphical models, such as Bayesian networks and Markov networks, represent joint distributions over a set of variables by means of a graph. When the graph is singly connected, local propagation rules of the sort proposed by Pearl (1988) are guaranteed to converge to the correct posterior probabilities. Recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops, but a theoretical understanding of this performance has yet to be achieved. <\/jats:p><jats:p> For graphical models with a single loop, we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals. Using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments (although the computed marginals will be incorrect). We also show how nodes can use local information in the messages they receive in order to correct their computed marginals. <\/jats:p><jats:p> We discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single-loop graphs may hold for a larger class of graphs. Specifically we discuss the implication of our results for understanding a class of recently proposed error-correcting codes known as turbo codes. <\/jats:p>","DOI":"10.1162\/089976600300015880","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:57:56Z","timestamp":1027771076000},"page":"1-41","source":"Crossref","is-referenced-by-count":251,"title":["Correctness of Local Probability Propagation in Graphical Models with Loops"],"prefix":"10.1162","volume":"12","author":[{"given":"Yair","family":"Weiss","sequence":"first","affiliation":[{"name":"Department of Brain and Cognitive Sciences, MIT, Cambridge, MA 02139, U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"p_2","author":"Aji S. M.","journal-title":"IEEE Trans. Inform. Theory. Available at: http:\/\/www.systems.caltech.edu\/ EE\/Faculty\/rjm."},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1984.4767596"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1109\/49.661110"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1109\/49.661103"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1109\/5.18626"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(97)01050-7"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.2.227"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976600300015880","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:48:29Z","timestamp":1615585709000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/12\/1\/1-41\/6325"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1,1]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,1,1]]}},"alternative-id":["10.1162\/089976600300015880"],"URL":"https:\/\/doi.org\/10.1162\/089976600300015880","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1,1]]}}}