Everything that can be learned about a causal structure with latent variables by observational and interventional probing schemes
What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between one variable being a causal parent of the other and the two variables sharing a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other. Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined by Evans (2016)). We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint probability distributions that can be realized by the other using a given probing scheme. (Equivalence of causal structures is the special case of mutual dominance.) Finally, we investigate to what extent one can weaken the probing schemes implemented on the visible variables and still have the same discrimination power as a maximally informative probing scheme.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Learning Causal Structure Distributions for Robust Planning
Structural causal models describe how the components of a robotic system interact. They provide both structural and functional information about the relationships that are present in the system. The structural informatio…
Measurement Dependence Inducing Latent Causal Models
We consider the task of causal structure learning over measurement dependence inducing latent (MeDIL) causal models. We show that this task can be framed in terms of the graph theoretic problem of finding edge clique cov…
Differentiable Causal Discovery For Latent Hierarchical Causal Models
Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their sca…
Causal DiscoveryOnline Causal Structure Learning in the Presence of Latent Variables
We present two online causal structure learning algorithms which can track changes in a causal structure and process data in a dynamic real-time manner. Standard causal structure learning algorithms assume that causal st…
Triad Constraints for Learning Causal Structure of Latent Variables
Learning causal structure from observational data has attracted much attention, and it is notoriously challenging to find the underlying structure in the presence of confounders (hidden direct common causes of two variab…