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