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Conditional Instrumental Variable Regression with Representation Learning for Causal Inference
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Proposes CBRL.CIV, a non-linear conditional-instrumental-variable regression method that learns a confounding-balancing representation of observed confounders to jointly balance the CIV-treatment and treatment-outcome distributions under unobserved confounding.
Problem
Estimating average causal effects from observational data with unobserved confounders when only a conditional instrumental variable (CIV) is available and relationships are non-linear, where the observed confounders are imbalanced across both CIV groups and treatment groups.
Approach
Uses a conditional IV (relaxing the unconfounded-instrument condition) and learns a representation of observed confounders with two IPM-based balance terms: one making the representation independent of the sampled CIV value and one making it independent of the estimated treatment, combined with two-stage (CIV, treatment) logistic regressions and separate outcome heads.
Key results
- On synthetic Syn-4-4 out-of-sample, CBRL.CIV achieves 0.14±0.05 ACE error versus 0.48±0.27 for the next best CBIV.
- On IHDP-2-2 out-of-sample, CBRL.CIV achieves 0.251±0.082 error versus 2.312±0.934 for CBIV.
- Ablation shows removing the CIV-regression balance term (CBRL) increases error (e.g., 0.56±0.33 vs 0.16±0.05 on Syn-4-4 at 8k).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CBRL.CIV instead of CBIV | ACE estimation · Synthetic datasets, within- and out-of-sample | ACE estimation error: 0.48±0.27 -> 0.14±0.05; 0.4±0.19 -> 0.14±0.03; 0.41±0.14 -> 0.12±0.03 | Helped |
| Use CBRL.CIV instead of CBIV | ACE estimation · IHDP and Twins, out-of-sample | ACE estimation error: IHDP: 2.312±0.934 -> 0.251±0.082; 1.349±0.452 -> 0.454±0.068; 2.846±0.490 -> 0.108±0.063; Twins: 0.033±0.011 -> 0.030±0. | Helped |
| Add CIV regression balance loss (Eq. 2) (ablation) | CBRL.CIV · Synthetic datasets, 6k | ACE estimation error: 0.48 ± 0.27 -> 0.14 ± 0.05; 0.40 ± 0.19 -> 0.14 ± 0.03; 0.41 ± 0.14 -> 0.12 ± 0.03 | Helped |
| Add CIV and treatment regression balance losses (Eqs. 2 and 4) (ablation) | CBRL.CIV · Synthetic datasets, 6k | ACE estimation error: 0.60 ± 0.38 -> 0.14 ± 0.05; 0.58 ± 0.31 -> 0.14 ± 0.03; 0.51 ± 0.25 -> 0.12 ± 0.03 | Helped |
| Set α and β to 0.1 rather than 0 (ablation) | CBRL.CIV · Syn-4-4, 6k, within-sample | ACE estimation error: 0.1594 ± 0.0371 -> 0.1406 ± 0.0533 | Helped |
| Set α and β to 1 or 10 rather than 0.1 (ablation) | CBRL.CIV · Syn-4-4, 6k, within-sample | ACE estimation error: 0.1406 ± 0.0533 -> 0.1877 ± 0.0691; 0.1406 ± 0.0533 -> 0.2198 ± 0.0511 | Hurt |
Surprising findings
- Appendix reports that CBRL.CIV with alpha=beta=0 still gives small error, suggesting the balancing terms contribute less than the main text implies on some settings.
- Reported CBRL.CIV error values are identical across within- and out-of-sample on synthetic data in the main table, which is unusual.
Limitations
- Assumes a binary CIV and binary treatment; the method is evaluated only in simulated or semi-synthetic settings.
- Relies on the IV positivity and independent compliance type assumptions and on the conditioning set being pre-IV variables.
- Theoretical identification argument relies on assumed independence of sampled S-hat/W-hat and representation rather than a full proof of finite-sample consistency.
Experimental setup
Datasets: synthetic data (Syn-4-4, Syn-8-8, Syn-12-12) IHDP Twins
Benchmarks: synthetic Syn-4-4/Syn-8-8/Syn-12-12 IHDP-2-2/4-4/6-6 (semi-synthetic) Twins-2-2/4-4/6-6 (semi-synthetic)
Metrics: absolute ACE estimation error (mean ± STD)
Baselines: CBIV DeepIV OrthIV DMLIV DRIV SDRIV ForestDRIV CFR
Builds on: CBIV CFR DeepIV two-stage least squares
Closest papers by meaning
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