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Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder
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Proposes conditional front-door adjustment with an identifiable VAE (CFDiVAE) that learns a latent mediator from its proxies to estimate ATE under unobserved confounding.
Problem
Causal effect estimation from observational data when unobserved confounders exist and the standard front-door criterion is too restrictive to hold in practice.
Approach
Relaxes the standard front-door criterion to a conditional front-door criterion that allows the observed confounder W to interact with the mediator, proves identifiability of the resulting adjustment formula, and learns the latent CFD variable from its proxy with an identifiable VAE conditioned on T and W.
Key results
- CFDiVAE reaches 2.14% estimation bias at N=20k and about 2-3% for N from 6k to 10k, while back-door baselines stay around 20-22% bias.
- CFDiVAE bias stays around 3% across causal strengths of the unobserved confounder, while comparison methods degrade as confounding grows.
- On Adult, CFDiVAE estimates the causal effect of sex on income as 0.176, consistent with prior finding of significant indirect discrimination.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use conditional front-door adjustment and learn the CFD representation rather than use back-door baseline KernelDML | ATE estimation · Synthetic datasets, N=20k | estimation bias (%): 20.27 ± 0.94 -> 2.14 ± 3.38 | Helped |
| match learned representation dimension to ground-truth CFD dimension 2 rather than set it to 1 (ablation) | CFDiVAE · Ground-truth CFD dimension 2, N=20k | estimation bias (%): 9.88 ± 1.36 -> 4.16 ± 8.90 | Helped |
| match learned representation dimension to ground-truth CFD dimension 4 rather than set it to 1 (ablation) | CFDiVAE · Ground-truth CFD dimension 4, N=20k | estimation bias (%): 14.83 ± 1.74 -> 4.45 ± 1.75 | Helped |
| match learned representation dimension to ground-truth CFD dimension 8 rather than set it to 1 (ablation) | CFDiVAE · Ground-truth CFD dimension 8, N=20k | estimation bias (%): 17.65 ± 2.29 -> 7.42 ± 3.14 | Helped |
| use both T and W rather than W alone as additional observed variables (ablation) | CFDiVAE · Model identifiability analysis, N=20k | estimation bias (%): 1.69 ± 1.55 -> 1.57 ± 1.32 | Helped |
| use both T and W rather than T alone as additional observed variables (ablation) | CFDiVAE · Model identifiability analysis, N=20k | estimation bias (%): 1.77 ± 1.41 -> 1.57 ± 1.32 | Helped |
| add W to the additional observed variables used by T-CFDiVAE (ablation) | CFDiVAE · Model identifiability analysis, N=20k | estimation bias (%): 1.77 ± 1.41 -> 1.69 ± 1.55 | Helped |
| remove both T and W as additional observed variables (ablation) | CFDiVAE · Model identifiability analysis, N=20k | estimation bias (%): 1.57 ± 1.32 -> 4.55 ± 9.19 | Hurt |
| increase the strength of unobserved confounding along U to Y (ablation) | back-door comparison methods · Synthetic datasets, N=10k | estimation bias (%) | Hurt |
| increase the strength of unobserved confounding along U to Y (ablation) | CFDiVAE · Synthetic datasets, N=10k | estimation bias (%) | No clear effect |
Surprising findings
- At small sample sizes (0.5k), CFDiVAE has high bias (86.29%), worse than the back-door baselines like KernelDML (19.57%).
Limitations
- Relies on assumptions (separable W and proxy X, injective decoder, faithfulness) that may fail in practice.
- High estimation bias at small sample sizes (0.5k-1k) for CFDiVAE.
- ATE estimation step is derived only for linear models.
Experimental setup
Datasets: synthetic datasets generated from the paper's causal graph UCI Adult
Benchmarks: synthetic causal datasets (0.5k-20k samples) UCI Adult
Metrics: estimation bias (%) density comparison of learned representation
Baselines: LinearDRL CausalForest ForestDRL XLearner KernelDML CEVAE TEDVAE
Builds on: front-door adjustment identifiable VAE CEVAE TEDVAE
Closest papers by meaning
- Unified Covariate Adjustment for Causal Inference (NeurIPS 2024 · similarity 0.89)
- Identifiability Guarantees for Causal Disentanglement from Purely Observational Data (NeurIPS 2024 · similarity 0.89)
- Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimand (NeurIPS 2024 · similarity 0.89)
- Learning Linear Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity (NeurIPS 2024 · similarity 0.89)
- Coupling Generative Modeling and an Autoencoder with the Causal Bridge (NeurIPS 2025 · similarity 0.89)
- Marginal Causal Flows for Validation and Inference (NeurIPS 2024 · similarity 0.88)
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