Your Assumed DAG is Wrong and Here's How To Deal With It

TL;DR

This paper introduces a gradient-based method to estimate bounds on causal queries that accounts for uncertainty in the assumed DAG, improving robustness when prior causal knowledge is imperfect or disputed.

Contribution

It proposes an efficient optimization technique to derive bounds over a set of plausible causal graphs, addressing limitations of existing methods that rely on a single DAG assumption.

Findings

Achieves good coverage and sharpness for causal queries in synthetic and real data.

Provides bounds that are robust to inaccuracies in prior causal assumptions.

Offers a practical tool for causal inference under uncertain DAG assumptions.

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; 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?'.