Research map / Probabilistic and scientific modeling / Treatment effects
Hierarchical and Density-based Causal Clustering
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Extends causal k-means clustering of counterfactual mean vectors to hierarchical (robust inductive single/average/complete linkage) and density-based (level-set/Rips graph) clustering via plug-in nuisance estimates, with rate results showing the extra cost is the outcome regression estimation error.
Problem
Causal clustering of treatment effect heterogeneity via k-means needs strong margin/structural conditions on the outcome process and cannot handle non-spherical or varying-density clusters; hierarchical and density-based alternatives lack theory in this setting.
Approach
Plug-in causal clustering: estimate counterfactual regression functions mu_a(X), then apply off-the-shelf hierarchical (robust inductive hierarchical clustering) or density-based (kernel density level-set / Rips graph) clustering to the estimated mean vectors, with theory showing the error inflation equals the nuisance estimation error under minimal conditions.
Key results
- Simulation shows hierarchical causal clustering classification error increases with the effective alpha due to nuisance estimation error, consistent with Theorem on inflated good-neighborhood parameter.
- Density-based simulation with Gaussian mixture shows average Hausdorff distance between estimated and true level sets shrinks as n grows, with rate tied to outcome regression error.
- Voting study finds two clusters (~4% noise) with one cluster showing negative effect and higher baseline risk mu_0; employment data reveals four clusters with substantial heterogeneity.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add nuisance estimation error to the counterfactual mean estimates | Hierarchical causal clustering · Hierarchical clustering simulation | classification error | Hurt |
| Add nuisance estimation error to the counterfactual mean estimates | Density-based causal clustering · Density-based clustering simulation | Hausdorff distance | Hurt |
Limitations
- Rates for nonparametric outcome regression can be arbitrarily slow in high-dimensional covariates; semiparametric estimators not yet developed.
- Limited to the no-unmeasured-confounding identification strategy.
- Causal clustering is more descriptive/discovery-based than prescriptive for treatment decisions.
Experimental setup
Datasets: voting study dataset (semi-synthetic) US Bureau of Labor Statistics employment projections
Metrics: classification error Hausdorff distance between level sets
Baselines: causal k-means clustering
Builds on: causal k-means clustering robust hierarchical clustering (inductive, good-neighborhood) level-set density clustering Super Learner
Closest papers by meaning
- Causal Mixture Models: Characterization and Discovery (NeurIPS 2025 · similarity 0.89)
- On Heterogeneous Treatment Effects in Heterogeneous Causal Graphs (ICML 2023 · similarity 0.89)
- Learning Subgroups with Maximum Treatment Effects Without Causal Heuristics (AAAI 2026 · similarity 0.88)
- Doubly robust identification of treatment effects from multiple environments (ICLR 2025 · similarity 0.87)
- Do Contemporary Causal Inference Models Capture Real-World Heterogeneity? Findings from a Large-Scale Benchmark (ICLR 2025 · similarity 0.87)
- Data Fusion for Partial Identification of Causal Effects (NeurIPS 2025 · similarity 0.86)
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