Intervention Efficient Algorithms for Approximate Learning of Causal Graphs
This work provides more efficient algorithms for researchers and practitioners in causal inference who need to learn causal relationships from observational data with minimal intervention costs, especially when exact solutions are intractable.
This paper addresses the challenge of learning causal graphs with latent variables while minimizing intervention costs. The authors propose a bi-criteria approximation goal that allows for recovering all but εn^2 edges, achieving intervention costs within a small constant factor of the optimal.
We study the problem of learning the causal relationships between a set of observed variables in the presence of latents, while minimizing the cost of interventions on the observed variables. We assume access to an undirected graph $G$ on the observed variables whose edges represent either all direct causal relationships or, less restrictively, a superset of causal relationships (identified, e.g., via conditional independence tests or a domain expert). Our goal is to recover the directions of all causal or ancestral relations in $G$, via a minimum cost set of interventions. It is known that constructing an exact minimum cost intervention set for an arbitrary graph $G$ is NP-hard. We further argue that, conditioned on the hardness of approximate graph coloring, no polynomial time algorithm can achieve an approximation factor better than $Θ(\log n)$, where $n$ is the number of observed variables in $G$. To overcome this limitation, we introduce a bi-criteria approximation goal that lets us recover the directions of all but $εn^2$ edges in $G$, for some specified error parameter $ε> 0$. Under this relaxed goal, we give polynomial time algorithms that achieve intervention cost within a small constant factor of the optimal. Our algorithms combine work on efficient intervention design and the design of low-cost separating set systems, with ideas from the literature on graph property testing.