{"paper":{"title":"A Theoretical Analysis of the BDeu Scores in Bayesian Network Structure Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.LG","authors_text":"Joe Suzuki","submitted_at":"2016-07-15T09:22:55Z","abstract_excerpt":"In Bayesian network structure learning (BNSL), we need the prior probability over structures and parameters. If the former is the uniform distribution, the latter determines the correctness of BNSL. In this paper, we compare BDeu (Bayesian Dirichlet equivalent uniform) and Jeffreys' prior w.r.t. their consistency. When we seek a parent set $U$ of a variable $X$, we require regularity that if $H(X|U)\\leq H(X|U')$ and $U\\subsetneq U'$, then $U$ should be chosen rather than $U'$. We prove that the BDeu scores violate the property and cause fatal situations in BNSL. This is because for the BDeu sc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04427","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}