Certifying Interventional Agreement Among Observationally Equivalent Causal Models

Sourena Khanzadeh, Daniel Platnick, Marjan Alirezaie, Hossein Rahnama

Observationally equivalent causal models can still disagree about what happens under intervention, because interventions create inputs that never occur in observational data. We introduce Interventional Separation Selection (ISS), which repeatedly queries the true system with an admissible intervention on which the surviving candidate models disagree, discards the candidates the outcome contradicts, and stops once no intervention within a cost bound separates the survivors. If the true system is among the candidates, this stopping condition certifies that every survivor agrees with it on every admissible intervention within the bound, a guarantee that no observational learner can give, however much data it sees. The stopping condition depends only on the survivors, so it can be checked without knowing the truth. For continuous variables the candidates form an infinite version space, and mixed-integer linear programs decide the stopping condition exactly over all of it, with agreement holding up to a tolerance. On a three-digit colored MNIST causal abstraction task in which ink hue tracks digit size, plain convolutional networks trained on examples reach zero held-out error, yet…