Improving Efficiency and Accuracy of Causal Discovery Using a Hierarchical Wrapper

Abstract

Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete causal discovery algorithms have been previously introduced, where a directed acyclic graph (DAG), or its equivalence class, representing causal relations is searched. However, in real-world cases, only finite training data is available, which limits the power of statistical tests used by these algorithms, leading to errors in the inferred causal model. This is commonly addressed by devising a strategy for using as few as possible statistical tests. In this paper, we introduce such a strategy in the form of a recursive wrapper for existing constraint-based causal discovery algorithms, which preserves soundness and completeness. It recursively clusters the observed variables using the normalized min-cut criterion from the outset, and uses a baseline causal discovery algorithm during backtracking for learning local sub-graphs. It then combines them and ensures completeness. By an ablation study, using synthetic data, and by common real-world benchmarks, we demonstrate that our approach requires significantly fewer statistical tests, learns more accurate graphs, and requires shorter run-times than the baseline algorithm.

Clustering and Structural Robustness in Causal Diagrams

“…The back-door criterion (Pearl, 1993), the front-door criterion (Pearl, 1995), and ignorability assumptions in the potential outcome framework (Rosenbaum and Rubin, 1983) impose conditions upon a set (i.e., a cluster) of variables and the structure inside the set is not important. Explicitly, clusters have been constructed starting from structural equations (Skorstad, 1990) or multivariate data (Entner and Hoyer, 2012;Parviainen and Kaski, 2017;Nisimov et al, 2021). Outside causal inference, many clustering methods for directed graphs have been proposed under varying premises (Malliaros and Vazirgiannis, 2013).…”