Research map / Probabilistic and scientific modeling / Treatment effects
Learning Representations of Instruments for Partial Identification of Treatment Effects
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Learns a neural discrete partitioning of complex (high-dimensional, continuous) instruments to yield valid and tight partial-identification bounds on the CATE with binary treatments, avoiding adversarial training.
Problem
Estimating valid and informative bounds on the conditional average treatment effect from observational data with unobserved confounding, when instruments are complex (continuous, high-dimensional, e.g. genetic data) rather than discrete or binary.
Approach
Map instruments to a discrete latent representation via a Gumbel-softmax neural partitioner, then compute closed-form discrete-instrument CATE bounds on top of it; the representation is trained end-to-end to minimize bound width while a regularizer keeps partition probabilities above a threshold to control finite-sample variance.
Key results
- On Dataset 2, the proposed method reaches width 1.13 ± 0.19 at k=2 versus 1.34 ± 0.19 for the naive baseline, with both achieving 100% coverage.
- On the high-dimensional Dataset 3, MSD across k drops to 0.03 ± 0.02 for the proposed method versus 0.10 ± 0.10 for the naive baseline.
- Both methods achieve 100% coverage in nearly all settings, supporting bound validity in simulations.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learn the instrument representation to tighten bounds rather than use k-means discretization | CATE bounds method · Dataset 2 | width: 1.34 ± 0.19 -> 1.13 ± 0.19 (k=2); 1.28 ± 0.20 -> 1.15 ± 0.31 (k=3) | Helped |
| Learn the instrument representation to tighten bounds rather than use k-means discretization | CATE bounds method · Dataset 3 | width: 1.96 ± 0.05 -> 1.87 ± 0.05 (k=2); 1.91 ± 0.03 -> 1.87 ± 0.08 (k=4); 1.74 ± 0.26 -> 1.85 ± 0.06 (k=6) | Helped |
| Learn the instrument representation to tighten bounds rather than use k-means discretization | CATE bounds method · Dataset 1 | width: 1.62 ± 0.06 -> 1.01 ± 0.05 (k=2); 0.83 ± 0.16 -> 1.09 ± 0.04 (k=3) | Mixed |
| Learn representations with the proposed method rather than k-means discretization | CATE bounds method · Dataset 1 | MSD(k): 0.28 ± 0.06 -> 0.03 ± 0.03 | Helped |
| Learn representations with the proposed method rather than k-means discretization | CATE bounds method · Dataset 2 | MSD(k): 0.09 ± 0.06 -> 0.06 ± 0.06 | Helped |
| Learn representations with the proposed method rather than k-means discretization | CATE bounds method · Dataset 3 | MSD(k): 0.10 ± 0.10 -> 0.03 ± 0.02 | Helped |
| Vary the number of discretizations from k=2 to k=3 (ablation) | Naïve CATE bounds · Dataset 1 | width: 1.62 ± 0.06 -> 0.83 ± 0.16 | Helped |
| Vary the number of discretizations from k=2 to k=3 (ablation) | Ours CATE bounds · Dataset 1 | width: 1.01 ± 0.05 -> 1.09 ± 0.04 | Hurt |
| Vary the number of discretizations from k=2 to k=3 (ablation) | Naïve CATE bounds · Dataset 2 | width: 1.34 ± 0.19 -> 1.28 ± 0.20 | Helped |
| Vary the number of discretizations from k=2 to k=3 (ablation) | Ours CATE bounds · Dataset 2 | width: 1.13 ± 0.19 -> 1.15 ± 0.31 | Hurt |
| Add the auxiliary guidance loss | Representation network · Training stability | training stability | Helped |
Surprising findings
- The naive k-means baseline produced falsely overconfident bounds at k=6 on Dataset 3, with oracle coverage dropping to 0.75.
Limitations
- Relies on standard IV assumptions (exclusion, independence) that are not testable in general
- Evaluated only on simulated data with known CATE; no real-world MR dataset
- No direct comparison with existing methods because they are not tailored to the binary-treatment, complex-instrument setting
Experimental setup
Datasets: Simulated Dataset 1 (1D continuous polygenic-risk-style instrument) Simulated Dataset 2 (complex propensity score) Simulated Dataset 3 (20 binary SNP-like instruments)
Benchmarks: Simulated Datasets 1-3
Metrics: coverage average bound width mean squared difference across k (MSD) MSE vs oracle bounds
Baselines: Naive k-means discretization followed by discrete-IV bounds
Builds on: closed-form partial identification bounds for discrete instruments (Balke-Pearl Gumbel-softmax
Closest papers by meaning
- Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments (ICML 2024 · similarity 0.92)
- Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation (ICLR 2024 · similarity 0.91)
- Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data (NeurIPS 2024 · similarity 0.89)
- Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner (NeurIPS 2024 · similarity 0.89)
- A Non-parametric Direct Learning Approach to Heterogeneous Treatment Effect Estimation under Unmeasured Confounding (NeurIPS 2024 · similarity 0.89)
- Treatment Effect Estimation for Optimal Decision-Making (NeurIPS 2025 · similarity 0.88)
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