Efficient Intervention Design for Causal Discovery with Latents
This work addresses the challenge of efficient causal discovery in the presence of latent variables, which is incremental as it builds on existing methods by introducing new cost models and algorithms.
The paper tackles the problem of recovering causal graphs with latent variables while minimizing intervention costs, presenting algorithms that achieve within a 2-factor of optimal cost under a linear model and provide bounds on the number of interventions needed under an identity cost model.
We consider recovering a causal graph in presence of latent variables, where we seek to minimize the cost of interventions used in the recovery process. We consider two intervention cost models: (1) a linear cost model where the cost of an intervention on a subset of variables has a linear form, and (2) an identity cost model where the cost of an intervention is the same, regardless of what variables it is on, i.e., the goal is just to minimize the number of interventions. Under the linear cost model, we give an algorithm to identify the ancestral relations of the underlying causal graph, achieving within a $2$-factor of the optimal intervention cost. This approximation factor can be improved to $1+ε$ for any $ε> 0$ under some mild restrictions. Under the identity cost model, we bound the number of interventions needed to recover the entire causal graph, including the latent variables, using a parameterization of the causal graph through a special type of colliders. In particular, we introduce the notion of $p$-colliders, that are colliders between pair of nodes arising from a specific type of conditioning in the causal graph, and provide an upper bound on the number of interventions as a function of the maximum number of $p$-colliders between any two nodes in the causal graph.