Research map / Probabilistic and scientific modeling / Treatment effects
Learning Shadow Variable Representation for Treatment Effect Estimation under Collider Bias
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes ShadowCatcher, which learns shadow-variable representations from observed covariates using conditional-independence constraints and a hypothesis tester, and ShadowEstimator, a CATE estimator that uses them to correct collider bias.
Problem
Estimating treatment effects from observational data under collider bias (sample selection induced by both treatment and outcome), which requires valid shadow variables that are hard to find without expert knowledge.
Approach
Automatically generate representations of observed covariates that satisfy the shadow-variable assumptions (outcome dependence given X,T,S=1 and independence from selection given X,T,Y), verifying them with a refutation-based hypothesis test, and plug them into a shadow-variable-based odds-ratio estimator for CATE.
Key results
- On synthetic data with beta=1, ShadowCatcher-based OURS achieves sqrt(PEHE) of 0.227 on selected data vs. 0.284 for the best baseline DR-CFR and 0.289 for ES-CFR (selected data).
- On IHDP within-sample, OURS achieves sqrt(PEHE) 0.703±0.106 vs. 1.193 for DESCN (best baseline).
- On Jobs, OURS achieves within-sample policy risk 0.279±0.017, the lowest among methods (best baseline IPSW-like values around 0.284–0.290 and ES-CFR 0.290).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ShadowCatcher-learned shadow representations and ShadowEstimator | CATE estimation under collider bias · Synthetic datasets, β = 1, 3, and 5; selected and unselected data | √PEHE: OURS: 0.227±0.001, 0.229±0.001 (β = 1); 0.249±0.013, 0.255±0.021 (β = 3); 0.299±0.008, 0.300±0.008 (β = 5) | Helped |
| Use ShadowCatcher-learned shadow representations and ShadowEstimator | CATE estimation under collider bias · IHDP, within-sample and out-of-sample | √PEHE: 0.703±0.106, 0.723±0.102 | Helped |
| Use ShadowCatcher-learned shadow representations and ShadowEstimator | CATE estimation under collider bias · ACIC 2016, within-sample and out-of-sample | √PEHE: 1.911±0.126, 2.047±0.351 | Helped |
| Use ShadowCatcher-learned shadow representations and ShadowEstimator | Treatment policy estimation · JOBS, within-sample and out-of-sample | RPol: 0.279±0.017, 0.280±0.018 | Helped |
| Remove the conditional-dependence constraint from ShadowCatcher (ablation) | ShadowCatcher · Synthetic data | CATE estimation performance | Hurt |
| Remove the hypothesis tester that guarantees the conditional-independence constraint (ablation) | ShadowCatcher · Synthetic data | CATE estimation performance | Hurt |
| Lower the reject threshold α (ablation) | ShadowCatcher · Synthetic data with ds = 0.9·d and β = 1 | √PEHE | Helped |
| Lower the reject threshold α (ablation) | ShadowCatcher · Synthetic data with ds = 0.9·d and β = 1 | number of iterations | Hurt |
Surprising findings
- Heckit and IPSW perform poorly because they only address selection driven by X and T and cannot handle collider bias from T→S←Y.
Limitations
- Choice of rejection threshold alpha trades off efficiency (iterations) against performance.
- Performance depends on whether covariates contain latent information satisfying the shadow-variable assumption and on covariates being involved in sample selection.
- Relies on the identification assumptions of shadow variables; no baseline handles collider bias without extra assumptions.
Experimental setup
Datasets: IHDP ACIC 2016 Jobs synthetic collider-bias data
Benchmarks: IHDP ACIC 2016 Jobs synthetic collider-bias data
Metrics: sqrt(PEHE) policy risk
Baselines: Heckit Doubly Robust IPSW BNN TARNet CFR CForest DR-CFR TEDVAE DeR-CFR DESCN ES-CFR
Builds on: shadow variable identification (d'Haultfoeuille 2010; Miao & Tchetgen Tchetgen 2 CFR Heckman correction
Closest papers by meaning
- A Generative Approach for Treatment Effect Estimation under Collider Bias: From an Out-of-Distribution Perspective (ICML 2024 · similarity 0.90)
- Two-Stage Shadow Inclusion Estimation: An IV Approach for Causal Inference under Latent Confounding and Collider Bias (ICML 2024 · similarity 0.89)
- Learning Representations of Instruments for Partial Identification of Treatment Effects (ICML 2025 · similarity 0.86)
- Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation (ICLR 2024 · similarity 0.86)
- Doubly robust identification of treatment effects from multiple environments (ICLR 2025 · similarity 0.86)
- Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments (ICML 2024 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.