Date of Original Version

7-2013

Type

Conference Proceeding

Rights Management

Copyright © 2013 by AUAI Press

Abstract or Description

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 to data generated by a wider class of causal models that may contain non-linear and cyclic relations among the latent variables.

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Published In

Proceedings of the Conference on Uncertainly in Artificial Intelligence (UAI), 2013.