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Detecting and Measuring Confounding Using Causal Mechanism Shifts
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Proposes three confounding measures (CNF-1/2/3) that detect and quantify observed and unobserved confounding between variables using multi-context data with sparse causal mechanism shifts, without causal sufficiency or parametric assumptions.
Problem
Detecting and measuring confounding (observed and unobserved) among variables from observational data across multiple contexts, without assuming causal sufficiency or parametric causal models.
Approach
Defines confounding measures based on directed information and conditional directed information (CNF-1, using hard interventions), mutual information between context-wise expectations induced by mechanism shifts of confounders (CNF-2), and a variant using known causal direction (CNF-3); extends to conditional and joint confounding via total correlation and proves properties (positivity, monotonici
Key results
- On Erdos-Renyi binary graphs with 10-25 nodes, the three settings achieve recall up to 1.0 and F1 between 0.74 and 0.91 depending on setting and size.
- In three-node simulations, measured confounding is near zero for non-confounded graphs and positive for confounded graphs; controlling for the detected confounder reduces causal effect estimation error (e.g., G3 bias drops from about 0.55 to about 0.01-0.06).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Control for variables identified as confounders | Causal-effect estimation on G3 and G4 · G3 and G4, sample sizes 1000, 2000, 3000, 4000, and 5000 | Absolute difference between true and estimated causal effects: G3: 0.55 -> 0.06 (1000), 0.57 -> 0.02 (2000), 0.55 -> 0.007 (3000), 0.52 -> 0.03 (4000), 0.52 -> 0.009 (5000); G4: 0.24 | Helped |
Limitations
- Number of contexts required can be large since many contexts are discarded.
- Different measures (CNF-1/2/3) may yield different values for the same pair, so they are meant for relative comparison rather than point comparison.
- Experiments are limited to simulations; no real-world datasets are analyzed.
Experimental setup
Datasets: synthetic linear-Gaussian three-node graphs synthetic Erdos-Renyi binary causal graphs
Metrics: precision recall F1 absolute bias of causal effect estimate
Builds on: directed information sparse mechanism shift independent causal mechanisms nested Markov models
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- Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms (ICML 2025 · similarity 0.87)
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