The paper formalizes distinct notions of identifiability over collections of causal diagrams and proves a hierarchy among them, leaving an open conjecture on the gap between two central notions.
Towards Computing an Optimal Abstraction for Structural Causal Models
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abstract
Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we focus on the problem of learning abstractions. We start by defining the learning problem formally in terms of the optimization of a standard measure of consistency. We then point out the limitation of this approach, and we suggest extending the objective function with a term accounting for information loss. We suggest a concrete measure of information loss, and we illustrate its contribution to learning new abstractions.
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Identifiability in Causal Abstractions: A Hierarchy of Criteria
The paper formalizes distinct notions of identifiability over collections of causal diagrams and proves a hierarchy among them, leaving an open conjecture on the gap between two central notions.