Universität zu Köln

Kela, Aditya, von Prillwitz, Kai, Aberg, Johan, Chaves, Rafael ORCID: 0000-0001-8493-4019 and Gross, David (2020). Semidefinite Tests for Latent Causal Structures. IEEE Trans. Inf. Theory, 66 (1). S. 339 - 350. PISCATAWAY: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. ISSN 1557-9654

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Abstract

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures where all correlations between observed quantities are solely due to the influence from latent variables. We show that each model of this type imposes a certain signature on the observable covariance matrix in terms of a particular decomposition into positive semidefinite components. This signature, and thus the underlying hypothetical latent structure, can be tested in a computationally efficient manner via semidefinite programming. This stands in stark contrast with the algebraic geometric tools required if the full observable probability distribution is taken into account. The semidefinite test is compared with tests based on entropic inequalities.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kela, Aditya UNSPECIFIED UNSPECIFIED UNSPECIFIED von Prillwitz, Kai UNSPECIFIED UNSPECIFIED UNSPECIFIED Aberg, Johan UNSPECIFIED UNSPECIFIED UNSPECIFIED Chaves, Rafael UNSPECIFIED orcid.org/0000-0001-8493-4019 UNSPECIFIED Gross, David UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-352281
DOI:	10.1109/TIT.2019.2935755
Journal or Publication Title:	IEEE Trans. Inf. Theory
Volume:	66
Number:	1
Page Range:	S. 339 - 350
Date:	2020
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Place of Publication:	PISCATAWAY
ISSN:	1557-9654
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language GEOMETRY Multiple languages Computer Science, Information Systems; Engineering, Electrical & Electronic Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/35228