Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Selecting valid adjustment sets with uncertain causal graphs

Zhongyi Hu, Stéphanie van der Pas

TL;DR

This work tackles unbiased causal effect estimation when the exact DAG is unknown but the skeleton is known. It introduces a Bayesian graph-sampling approach over directed graphs to assess the validity of adjustment sets, leveraging local graph changes to rapidly test candidates and produce a compact, high-probability set of valid adjustments. Theoretical results characterize how valid adjustment sets behave under graph perturbations and under amenable CPDAGs, and the authors provide a concrete algorithm (Get_adjust) with complexity guarantees. Empirical results, including simulations and a Sachs dataset analysis, show improved precision and robust performance under graph misspecification, highlighting practical gains for estimating treatment effects when full causal structure is uncertain.

Abstract

Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge, introducing uncertainty. We present techniques to identify valid adjustment sets despite potential errors in the estimated causal graph. Specifically, we assume that only the skeleton of the DAG is known. Under a Bayesian framework, we place a prior on graphs and wish to sample graphs and compute the posterior probability of each set being valid; however, directly doing so is inefficient as the number of sets grows exponentially with the number of nodes in the DAG. We develop theory and techniques so that a limited number of sets are tested while the probability of finding valid adjustment sets remains high. Empirical results demonstrate the effectiveness of the method.

Selecting valid adjustment sets with uncertain causal graphs

TL;DR

This work tackles unbiased causal effect estimation when the exact DAG is unknown but the skeleton is known. It introduces a Bayesian graph-sampling approach over directed graphs to assess the validity of adjustment sets, leveraging local graph changes to rapidly test candidates and produce a compact, high-probability set of valid adjustments. Theoretical results characterize how valid adjustment sets behave under graph perturbations and under amenable CPDAGs, and the authors provide a concrete algorithm (Get_adjust) with complexity guarantees. Empirical results, including simulations and a Sachs dataset analysis, show improved precision and robust performance under graph misspecification, highlighting practical gains for estimating treatment effects when full causal structure is uncertain.

Abstract

Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge, introducing uncertainty. We present techniques to identify valid adjustment sets despite potential errors in the estimated causal graph. Specifically, we assume that only the skeleton of the DAG is known. Under a Bayesian framework, we place a prior on graphs and wish to sample graphs and compute the posterior probability of each set being valid; however, directly doing so is inefficient as the number of sets grows exponentially with the number of nodes in the DAG. We develop theory and techniques so that a limited number of sets are tested while the probability of finding valid adjustment sets remains high. Empirical results demonstrate the effectiveness of the method.

Paper Structure

This paper contains 21 sections, 9 theorems, 14 equations, 9 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Definitions
  4. Bayesian Set-Up
  5. Why not the bootstrap?
  6. Adjustment sets when the graph changes
  7. Insignificant nodes
  8. Targeted adjustment sets
  9. Listing efficient valid adjustment sets
  10. Algorithmic considerations
  11. Main graphical assumption
  12. Algorithm
  13. Complexity bound and consistency
  14. Experiments and real data analysis
  15. Simulation set-up and measure metrics
  16. ...and 6 more sections

Key Result

Proposition 3.1

Consider two DAGs ${\cal G}$ and ${\cal G}'$ such that in topological orderings only one node $z$ is altered. If the following are the same in both graphs: and then $A$ is a valid adjustment set in ${\cal G}$ if and only if it is valid in ${\cal G}'$.

Figures (9)

  • Figure 1: Graph for adjustment set examples.
  • Figure 2: Precision plot showing that similar graphs (in terms of SHD) tend to have similar valid adjustment sets.
  • Figure 3: Invalid adjustment set example
  • Figure 4: True MEC is not enough
  • Figure 5: Total run time per 100 DAGs as a function of the number of nodes, displaying a linear tendency.
  • ...and 4 more figures

Theorems & Definitions (27)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Proposition 3.1
  • proof
  • Lemma 3.2
  • proof
  • ...and 17 more