An Efficient Algorithm for Computing Interventional Distributions in Latent Variable Causal Models
This work addresses a computational bottleneck for researchers in causal inference, though it is incremental as it extends existing methods to a more general graph structure.
The paper tackles the problem of computing interventional distributions in latent variable causal models using acyclic directed mixed graphs (ADMGs), proposing an algorithm that generalizes variable elimination to this setting and showing it is exponential in the mixed graph generalization of treewidth.
Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and belief propagation take advantage of constraints embedded in this factorization to compute such densities efficiently. In this paper, we propose an algorithm which computes interventional distributions in latent variable causal models represented by acyclic directed mixed graphs(ADMGs). To compute these distributions efficiently, we take advantage of a recursive factorization which generalizes the usual Markov factorization for DAGs and the more recent factorization for ADMGs. Our algorithm can be viewed as a generalization of variable elimination to the mixed graph case. We show our algorithm is exponential in the mixed graph generalization of treewidth.