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Distribution-Conditioned Adversarial Variational Autoencoder for Valid Instrumental Variable Generation
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Proposes VIV, an adversarial variational autoencoder that generates valid instrumental variables in latent space from observed candidates without requiring any valid IV among them.
Problem
Instrumental-variable-based counterfactual prediction under hidden confounding needs valid IVs (relevance, exclusivity, exogeneity), but existing IV generation methods require valid IVs to be present in the candidate pool.
Approach
Builds a VAE on the Bayesian network of the causal graph (ELBO respecting relevance and exclusivity) and uses the VAE inference network as a GAN generator, with a permutation-based discriminator that pushes the joint latent distribution toward the product of marginals (total correlation) to enforce exogeneity.
Key results
- On Demands-0.5, VIV achieves in-sample MSE of 0.45 with Poly2SLS and 0.18 with DFIV, versus 1.27 and 0.22 for NoneIV's best-case comparisons, approaching TrueIV on several backbones.
- On Twins, VIV has the lowest average MSE (0.27 ± 0.08) across backbones versus 0.52 for ModeIV/UAS and 3.18 for AutoIV, close to TrueIV (0.18).
- Weighting-based IV generation methods (UAS, WAS, ModeIV) perform similarly to having no IV, indicating they fail without valid candidates.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use VIV-generated IVs instead of zero-vector IVs | Poly2SLS on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: >1000 -> 0.45(0.05) | Helped |
| Use VIV-generated IVs instead of zero-vector IVs | NN2SLS on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 1.26(0.17) -> 0.39(0.10) | Helped |
| Use VIV-generated IVs instead of zero-vector IVs | KernelIV on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 0.52(0.04) -> 0.36(0.06) | Helped |
| Use VIV-generated IVs instead of zero-vector IVs | DualIV on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: Nan -> 2.46(0.62) | Hurt |
| Use VIV-generated IVs instead of zero-vector IVs | DeepIV on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 0.22(0.02) -> 0.17(0.01) | Helped |
| Use VIV-generated IVs instead of zero-vector IVs | OneSIV on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 0.31(0.05) -> 0.34(0.03) | Hurt |
| Use VIV-generated IVs instead of zero-vector IVs | DFIV on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 0.63(0.15) -> 0.17(0.02) | Helped |
| Use VIV-generated IVs instead of zero-vector IVs | DeepGMM on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 1.26(0.04) -> 0.52(0.05) | Helped |
| Use VIV-generated IVs instead of zero-vector IVs | AGMM on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 1.25(0.09) -> 0.40(0.05) | Helped |
| Use VIV-generated IVs instead of zero-vector IVs | Average counterfactual prediction on Twins · Twins | Average MSE: 1.81(3.74) -> 0.27(0.08) | Helped |
| Use VIV-generated IVs rather than true IVs | DualIV on Demands-0.5 out-sample · Demands-0.5 out-sample | MSE: 4.35(1.35) -> 2.46(0.62) | Helped |
Surprising findings
- VIV and AutoIV outperform TrueIV with the DualIV backbone, attributed to the continuous IV representations.
Limitations
- Evaluated only on simulated and one semi-synthetic real-world dataset due to lack of real counterfactual datasets.
- VAE training may not reach global optima, so no guarantee the true model is recovered.
- Relies on additive noise and identification assumptions.
Experimental setup
Datasets: Demands (simulated, Hartford et al. 2017) Twins
Benchmarks: Demands-0.5 Twins
Metrics: MSE of counterfactual prediction on do(T) outcomes
Baselines: NoneIV UAS WAS ModeIV AutoIV GIV-EM TrueIV
Builds on: variational autoencoder VAE-GAN beta-TCVAE (permutation trick for total correlation) Wasserstein GAN 2SLS
Closest papers by meaning
- Causal Inference with Conditional Instruments Using Deep Generative Models (AAAI 2023 · similarity 0.86)
- Deep IV: A Flexible Approach for Counterfactual Prediction (ICML 2017 · similarity 0.86)
- Counterfactual Generative Modeling with Variational Causal Inference (ICLR 2025 · similarity 0.85)
- Transformers Handle Endogeneity in In-Context Linear Regression (ICLR 2025 · similarity 0.84)
- Adversarially Balanced Representation for Continuous Treatment Effect Estimation (AAAI 2024 · similarity 0.84)
- Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradients (NeurIPS 2024 · similarity 0.84)
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