Noisy-OR Models with Latent Confounding
This work addresses a specific challenge in causal inference for discrete-valued variables, offering a solution for scenarios with limited interventions, though it is incremental as it builds on prior linear model results.
The paper tackles the problem of identifying causal models with latent confounding when only one or a few variables are intervened on per experiment, showing that identifiability can be achieved for noisy-OR models and extended to allow negative influences, with algorithms tested for accuracy, scalability, and robustness.
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.