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

2025-02-24

AI Summary

In causal inference, prior knowledge is often encoded as a single directed acyclic graph (DAG), yet such an assumption is frequently misspecified in practice. Method: We propose a robust causal effect estimation framework that does not rely on a single deterministic DAG. Instead, we introduce the first differentiable gradient-based optimization framework operating over a large set of DAGs compatible with prior knowledge. Our approach jointly enforces causal graph constraints and linear or nonlinear structural equation models, and efficiently computes tight upper and lower bounds on causal queries—e.g., the average treatment effect—via boundary propagation. Contribution/Results: Compared to conventional methods based on a single DAG or a Markov equivalence class, our framework achieves significantly improved bound coverage and sharpness on both synthetic and real-world datasets. It provides a computationally tractable and empirically verifiable solution to the fundamental question: “How reliable are causal conclusions when the assumed DAG is incorrect?”

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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?'.

Problem

• Addressing uncertainty in assumed DAGs
• Providing bounds for causal queries
• Optimizing causal effect estimation accuracy

Innovation

• Gradient-based optimization method
• Bounds for causal queries
• Handles imperfect prior knowledge