Selecting Accurate Subgraphical Models from Possibly Inaccurate Graphical Models

Yi Han, Joseph Ramsey, Peter Spirtes

Keywords: causal discovery, subgraph evaluation

Abstract:

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.

Submission Number: 109