{"id":38950,"date":"2026-08-21T15:27:24","date_gmt":"2026-08-21T15:27:24","guid":{"rendered":"https:\/\/lamarr-institute.org\/publication\/high-order-markov-blanket-discovery-via-a-k-order-relaxation-of-the-faithfulness-assumption\/"},"modified":"2026-09-17T11:16:44","modified_gmt":"2026-09-17T11:16:44","slug":"high-order-markov-blanket-discovery-via-a-k-order-relaxation-of-the-faithfulness-assumption","status":"publish","type":"publication","link":"https:\/\/lamarr-institute.org\/de\/publication\/high-order-markov-blanket-discovery-via-a-k-order-relaxation-of-the-faithfulness-assumption\/","title":{"rendered":"High-Order Markov Blanket Discovery via a k-Order Relaxation of the Faithfulness Assumption"},"content":{"rendered":"<p>The problem of learning the graphical Markov blanket (MB) of a variable from data has applications in many areas such as structure learning for Bayesian networks and Markov random fields, causal discovery, and feature selection. However, a common assumption most methods make is that the conditional independencies in the distribution imply the same separation in the graphical structure &#8212; also known as the faithfulness assumption. Unfortunately, this assumption can be violated by higher-order dependencies such as XOR and parity-type relations, and &#8212; on finite samples &#8212; by empirical violations that, in extreme cases, even induce spurious dependencies absent from the true distribution. Therefore, in this paper we propose a {&#8222;k-order&#8220;} relaxation of the faithfulness assumption that captures parity type relationships between k+2 variables. We then propose a proof of concept algorithm called k-order Markov blanket (kOMB) that uses this relaxation for MB discovery. Finally, we empirically show how kOMB can recover the MB of a variable under both true and empirical violations of faithfulness.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The problem of learning the graphical Markov blanket (MB) of a variable from data has applications in many areas such as structure learning for Bayesian networks and Markov random fields, causal discovery, and feature selection. However, a common assumption most methods make is that the conditional independencies in the distribution imply the same separation in the graphical structure &#8212; also known as the faithfulness assumption. Unfortunately, this assumption can be [&hellip;]<\/p>\n","protected":false},"author":14,"featured_media":0,"template":"","meta":{"_acf_changed":false,"footnotes":""},"publication-type":[30],"class_list":["post-38950","publication","type-publication","status-publish","hentry","publication-type-article"],"acf":[],"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/38950","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/types\/publication"}],"author":[{"embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":0,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/38950\/revisions"}],"wp:attachment":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/media?parent=38950"}],"wp:term":[{"taxonomy":"publication-type","embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication-type?post=38950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}