Your Assumed DAG is Wrong And Here’s How To Deal With It

Kirtan Padh, Zhufeng Li, Cecilia Casolo, Niki Kilbertus

Keywords: partial identification, causal discovery

TL;DR: The paper shows how we can deal with uncertainty in the graph structure while estimating causal effects using DAGs

Abstract: 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, whereas causal discovery often only provides an equivalence class of DAGs, relies on untestable assumptions itself, or are sensitive to hyperparameter and threshold choices. We propose an efficient, gradient-based optimization method that provides bounds for causal queries over a collection of plausible causal graphs given prior knowledge that may still be too large for exhaustive enumeration. We demonstrate excellent coverage and sharpness of our bounds for causal queries such as average treatment effect estimation in linear and non-linear synthetic settings as well as on real-world data. Our approach is an easy-to-use and widely applicable rebuttal to the valid critique of `What if your assumed DAG is wrong?'.

Submission Number: 96