{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T03:51:53Z","timestamp":1774929113916,"version":"3.50.1"},"reference-count":52,"publisher":"MIT Press - Journals","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p> Bayesian networks have been widely used in many scientific fields for describing the conditional independence relationships for a large set of random variables. This letter proposes a novel algorithm, the so-called p-learning algorithm, for learning moral graphs for high-dimensional Bayesian networks. The moral graph is a Markov network representation of the Bayesian network and also the key to construction of the Bayesian network for constraint-based algorithms. The consistency of the p-learning algorithm is justified under the small- n, large- p scenario. The numerical results indicate that the p-learning algorithm significantly outperforms the existing ones, such as the PC, grow-shrink, incremental association, semi-interleaved hiton, hill-climbing, and max-min hill-climbing. Under the sparsity assumption, the p-learning algorithm has a computational complexity of O(p<jats:sup>2<\/jats:sup>) even in the worst case, while the existing algorithms have a computational complexity of O(p<jats:sup>3<\/jats:sup>) in the worst case. <\/jats:p>","DOI":"10.1162\/neco_a_01190","type":"journal-article","created":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T00:05:57Z","timestamp":1555113957000},"page":"1183-1214","source":"Crossref","is-referenced-by-count":9,"title":["Learning Moral Graphs in Construction of High-Dimensional Bayesian Networks for Mixed Data"],"prefix":"10.1162","volume":"31","author":[{"given":"Suwa","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Biostatistics, University of Florida, Gainesville, FL 32611, U.S.A."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bochao","family":"Jia","sequence":"additional","affiliation":[{"name":"Lilly Corporate Center, Eli Lilly and Company, Indianapolis, IN 46285, 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