Uncertainty in Artificial Intelligence
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Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Models
Peter Spirtes
Abstract:
The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this paper, I extend the Trek Separation Theorem in two ways: I prove that the same necessary and sufficient conditions apply even when the generating model is partially non-linear and contains some cycles. This justifies application of constraint-based causal search algorithms such as the BuildPureClusters algorithm (Silva et al. 2006) for discovering the causal structure of latent variable models to data generated by a wider class of causal models that may contain non-linear and cyclic relations among the latent variables.
Keywords:
Pages: 606-615
PS Link:
PDF Link: /papers/13/p606-spirtes.pdf
BibTex:
@INPROCEEDINGS{Spirtes13,
AUTHOR = "Peter Spirtes ",
TITLE = "Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Models",
BOOKTITLE = "Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "606--615"
}


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