TY - GEN

T1 - Testing edges by truncations

AU - Shpitser, Ilya

AU - Richardson, Thomas S.

AU - Robins, James M.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - We consider the problem of testing whether two variables should be adjacent (either due to a direct effect between them, or due to a hidden common cause) given an observational distribution, and a set of causal assumptions encoded as a causal diagram. In other words, given a set of edges in the diagram known to be true, we are interested in testing whether another edge ought to be in the diagram. In fully observable faithful models this problem can be easily solved with conditional independence tests. Latent variables make the problem significantly harder since they can imply certain non-adjacent variable pairs, namely those connected by so called inducing paths, are not independent conditioned on any set of variables. We characterizewhich variable pairs can be determined to be non-adjacent by a class of constraints due to dormant independence, that is conditional independence in identifiable interventional distributions. Furthermore, we show that particular operations on joint distributions, which we call truncations are sufficient for exhibiting these non-adjacencies.This suggests a causal discovery procedure taking advantage of these constraints in the latent variable case can restrict itself to truncations.

AB - We consider the problem of testing whether two variables should be adjacent (either due to a direct effect between them, or due to a hidden common cause) given an observational distribution, and a set of causal assumptions encoded as a causal diagram. In other words, given a set of edges in the diagram known to be true, we are interested in testing whether another edge ought to be in the diagram. In fully observable faithful models this problem can be easily solved with conditional independence tests. Latent variables make the problem significantly harder since they can imply certain non-adjacent variable pairs, namely those connected by so called inducing paths, are not independent conditioned on any set of variables. We characterizewhich variable pairs can be determined to be non-adjacent by a class of constraints due to dormant independence, that is conditional independence in identifiable interventional distributions. Furthermore, we show that particular operations on joint distributions, which we call truncations are sufficient for exhibiting these non-adjacencies.This suggests a causal discovery procedure taking advantage of these constraints in the latent variable case can restrict itself to truncations.

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M3 - Conference contribution

AN - SCOPUS:77953488455

SN - 9781577354260

T3 - IJCAI International Joint Conference on Artificial Intelligence

SP - 1957

EP - 1963

BT - IJCAI-09 - Proceedings of the 21st International Joint Conference on Artificial Intelligence

PB - International Joint Conferences on Artificial Intelligence

T2 - 21st International Joint Conference on Artificial Intelligence, IJCAI 2009

Y2 - 11 July 2009 through 16 July 2009

ER -