Sadeghi, K;
(2017)
Faithfulness of Probability Distributions and Graphs.
Journal of Machine Learning Research
, 18
(148)
pp. 1-29.
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Abstract
A main question in graphical models and causal inference is whether, given a probability distribution P (which is usually an underlying distribution of data), there is a graph (or graphs) to which P is faithful. The main goal of this paper is to provide a theoretical answer to this problem. We work with general independence models, which contain probabilistic independence models as a special case. We exploit a generalization of ordering, called preordering, of the nodes of (mixed) graphs. This allows us to provide sufficient conditions for a given independence model to be Markov to a graph with the minimum possible number of edges, and more importantly, necessary and sufficient conditions for a given probability distribution to be faithful to a graph. We present our results for the general case of mixed graphs, but specialize the definitions and results to the better-known subclasses of undirected (concentration) and bidirected (covariance) graphs as well as directed acyclic graphs.
Type: | Article |
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Title: | Faithfulness of Probability Distributions and Graphs |
Open access status: | An open access version is available from UCL Discovery |
Publisher version: | http://jmlr.org/papers/v18/17-275.html |
Language: | English |
Additional information: | ®2017 Kayvan Sadeghi. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v18/17-275.html. |
Keywords: | causal discovery, compositional graphoid, directed acyclic graph, faithfulness, graphical model selection, independence model, Markov property, mixed graph, structural learning |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10058840 |
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