Research map / Probabilistic and scientific modeling / Treatment effects
Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model
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Proposes a Bayesian partially linear model with Gaussian process priors on the treatment-effect function and nuisance function, giving a closed-form CATE posterior with a posterior consistency guarantee for small-sample uncertainty quantification.
Problem
Quantifying uncertainty in conditional average treatment effect (CATE) estimation when only small observational samples are available, where tree/neural methods give point estimates and frequentist DML confidence intervals lack finite-sample guarantees.
Approach
Places Gaussian process priors on both the treatment-effect function theta(x) and nuisance f(x) in a partially linear model Y = theta(X)T + f(X) + noise; marginalizing f removes confounding bias without propensity score estimation, yielding an analytic CATE posterior, prior-knowledge-driven kernels, and a posterior consistency theorem.
Key results
- On synthetic data with n=200/500, the proposed GP method achieved better or competitive CATE MSE than BCF and R Learner, outperforming both under Setup D (non-differentiable theta and f).
- On the ACIC semi-synthetic dataset, the R Learner with kernel regression had MSEs of 71.8 ± 11.0 (n=200) and 52.3 ± 4.3 (n=500), while the proposed method remained stable across Matérn and RBF kernels.
- With n small, the proposed method and BCF achieved higher interval coverage than R Learner while keeping interval lengths short.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use anisotropic covariance informed by prior knowledge that X1 is the treatment effect modifier instead of isotropic covariance (ablation) | Proposed method · Synthetic prior-knowledge experiment, n=100 | MSE: 0.240± 0.0745 -> 0.185± 0.188 | Helped |
| Use the proposed anisotropic GP model instead of Alaa+ | CATE estimation · Synthetic prior-knowledge experiment, n=100 | MSE: 0.244± 0.112 -> 0.185± 0.188 | Helped |
| Use the proposed method rather than BCF and R Learner | CATE estimation · Synthetic binary and continuous-valued treatment setups | MSE | Mixed |
| Use the proposed method rather than BCF and R Learner | CATE estimation · Synthetic Setup D | MSE | Helped |
| Use the proposed method rather than other methods | CATE estimation · Synthetic continuous-valued treatment Setup C | MSE | Hurt |
| Use kernel regression for the R Learner conditional expectation models | R Learner · ACIC, n=200 and n=500 | MSE: 71.8 ± 11.0 (n=200); 52.3± 4.3 (n=500) | Hurt |
| Use Bayesian methods rather than the R Learner for uncertainty intervals | Proposed method and BCF · Synthetic binary-treatment data | Coverage ratio | Helped |
Limitations
- Hyperparameters are set by marginal likelihood maximization rather than a full Bayesian treatment, so the theoretical consistency result does not cover the experimented hyperparameter selection.
- Cubic O(n^3) cost of exact GP inference; sparse approximations are suggested but not evaluated.
- Treatment-effect linearity in the basic model; nonlinear dose response h(T) must be specified by prior knowledge.
Experimental setup
Datasets: ACIC 2016 dataset (LBIDD-based semi-synthetic) synthetic partially linear DGPs (Setups A-D)
Benchmarks: ACIC dataset synthetic partially linear DGPs
Metrics: MSE of CATE coverage ratio of credible/confidence intervals interval length
Baselines: Bayesian causal forest (BCF) R Learner Bayesian linear regression stableCFR Alaa+ (causal multitask GP)
Builds on: R Learner Double/Debiased Machine Learning Bayesian causal forest Alaa et al. causal multitask Gaussian processes
Closest papers by meaning
- Limits of Estimating Heterogeneous Treatment Effects: Guidelines for Practical Algorithm Design (ICML 2018 · similarity 0.90)
- A Non-parametric Direct Learning Approach to Heterogeneous Treatment Effect Estimation under Unmeasured Confounding (NeurIPS 2024 · similarity 0.89)
- Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing (AAAI 2024 · similarity 0.86)
- Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner (NeurIPS 2024 · similarity 0.86)
- Conformal Inference of Individual Treatment Effects Using Conditional Density Estimates (AAAI 2025 · similarity 0.86)
- Do Contemporary Causal Inference Models Capture Real-World Heterogeneity? Findings from a Large-Scale Benchmark (ICLR 2025 · similarity 0.85)
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