2008-07-09-niepert08a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_editor	editor	bibtex_author	author	date	note	address	container-title	volume	genre	issued	pdf	extras
On the conditional independence implication problem: a lattice-theoretic approach	A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a finite, sound and complete inference system relative to semi-lattice inclusions is presented. This system is shown to be (1) sound and complete for saturated CI statements, (2) complete for general CI statements, and (3) sound and complete for stable CI statements. These results yield a criterion that can be used to falsify instances of the implication problem and several heuristics are derived that approximate this "lattice-exclusion" criterion in polynomial time. Finally, we provide experimental results that relate our work to results obtained from other existing inference algorithms.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	niepert08a	0	On the conditional independence implication problem: a lattice-theoretic approach	435	443	435-443	435	false	McAllester, David A. and Myllym{"a}ki, Petri	given family David A. McAllester given family Petri Myllymäki	Niepert, Mathias and Van Gucht, Dirk and Gyssens, Marc	given family Mathias Niepert given family Dirk Van Gucht given family Marc Gyssens	2008-07-09	Reissued by PMLR on 30 October 2024.		Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence	R6	inproceedings	date-parts 2008 7 9	http://proceedings.mlr.press/r6/niepert08a/niepert08a.pdf