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Given a set of experiments in which varying subsets of observed variables aresubject to intervention, we consider the problem of identifiability of causalmodels exhibiting latent confounding. While identifiability is trivial wheneach experiment intervenes on a large number of variables, the situation ismore complicated when only one or a few variables are subject to interventionper experiment. For linear causal models with latent variables Hyttinen et al.(2010) gave precise conditions for when such data are sufficient to identifythe full model. While their result cannot be extended to discrete-valuedvariables with arbitrary cause-effect relationships, we show that a similarresult can be obtained for the class of causal models whose conditionalprobability distributions are restricted to a `noisy-OR' parameterization. Wefurther show that identification is preserved under an extension of the modelthat allows for negative influences, and present learning algorithms that wetest for accuracy, scalability and robustness.

Noisy-OR Models with Latent Confounding