Selecting Accurate Subgraphical Models from Possibly Inaccurate Graphical Models

Methods of statistically testing the accuracy of causal graphical models have traditionally been limited, with most focusing on parametric global assessments of the entire causal graph. However, whether or not a causal graphical model passes a statistical test, it is crucial for many practical applications to find which parts of the graph are accurately reconstructed and which are not. In this paper, we introduce the Vertex Checker, the only statistical test that we are aware of that takes as input a causal graphical model G, a vertex X, and an alpha level, sample data, and a conditional independence test, and provides a non-parametric, asymptotically correct, statistical test of a local subgraph of X, is computationally feasible for dozens of variables, and is extendable to other kinds of causal graphical models. Through extensive simulations, we demonstrate the robustness of the Vertex Checker across various data types, causal graphs, and distributions both in terms of accuracy of graphical structure and of quantitative estimates of causal effects. Furthermore, we apply the Vertex Checker to the real-world Sachs dataset, showcasing its practical applicability in uncovering accurate substructures within causal graphs, even when the overall causal graphical model is rejected.