On Learning Causal Structures from Non-Experimental Data without Any Faithfulness Assumption
This work provides a theoretical justification for standard causal learning algorithms, impacting researchers in causal inference by showing that sacrificing convergence for some networks is unavoidable without faithfulness assumptions.
The paper addresses the challenge of learning causal structures from non-experimental data without relying on the faithfulness assumption, proving that any algorithm achieving the best possible convergence mode must converge to the truth for all causal Bayesian networks that satisfy faithfulness, making this a mandatory design practice.
Consider the problem of learning, from non-experimental data, the causal (Markov equivalence) structure of the true, unknown causal Bayesian network (CBN) on a given, fixed set of (categorical) variables. This learning problem is known to be so hard that there is no learning algorithm that converges to the truth for all possible CBNs (on the given set of variables). So the convergence property has to be sacrificed for some CBNs---but for which? In response, the standard practice has been to design and employ learning algorithms that secure the convergence property for at least all the CBNs that satisfy the famous faithfulness condition, which implies sacrificing the convergence property for some CBNs that violate the faithfulness condition (Spirtes et al. 2000). This standard design practice can be justified by assuming---that is, accepting on faith---that the true, unknown CBN satisfies the faithfulness condition. But the real question is this: Is it possible to explain, without assuming the faithfulness condition or any of its weaker variants, why it is mandatory rather than optional to follow the standard design practice? This paper aims to answer the above question in the affirmative. We first define an array of modes of convergence to the truth as desiderata that might or might not be achieved by a causal learning algorithm. Those modes of convergence concern (i) how pervasive the domain of convergence is on the space of all possible CBNs and (ii) how uniformly the convergence happens. Then we prove a result to the following effect: for any learning algorithm that tackles the causal learning problem in question, if it achieves the best achievable mode of convergence (considered in this paper), then it must follow the standard design practice of converging to the truth for at least all CBNs that satisfy the faithfulness condition---it is a requirement, not an option.