Your Assumed DAG is Wrong and Here's How To Deal With It
This addresses the issue of unreliable DAG assumptions in causal inference for researchers and practitioners, offering a practical rebuttal to critiques of model uncertainty, though it is incremental by building on existing methods to handle imperfect knowledge.
The paper tackles the problem of causal inference when prior knowledge about causal relationships is uncertain, by proposing a gradient-based optimization method that provides bounds for causal queries over a collection of graphs, achieving good coverage and sharpness in synthetic and real-world data.
Assuming a directed acyclic graph (DAG) that represents prior knowledge of causal relationships between variables is a common starting point for cause-effect estimation. Existing literature typically invokes hypothetical domain expert knowledge or causal discovery algorithms to justify this assumption. In practice, neither may propose a single DAG with high confidence. Domain experts are hesitant to rule out dependencies with certainty or have ongoing disputes about relationships; causal discovery often relies on untestable assumptions itself or only provides an equivalence class of DAGs and is commonly sensitive to hyperparameter and threshold choices. We propose an efficient, gradient-based optimization method that provides bounds for causal queries over a collection of causal graphs -- compatible with imperfect prior knowledge -- that may still be too large for exhaustive enumeration. Our bounds achieve good coverage and sharpness for causal queries such as average treatment effects in linear and non-linear synthetic settings as well as on real-world data. Our approach aims at providing an easy-to-use and widely applicable rebuttal to the valid critique of `What if your assumed DAG is wrong?'.