# Hierarchical and Density-based Causal Clustering

arXiv: https://arxiv.org/abs/2411.01250 · HTML: https://mlsanity.com/paper/2411.01250/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 64 references that are in the map.
- First posted on arXiv 2 Nov 2024.

## Builds on (most cited first, 18 of 18)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [Nonparametric causal effects based on incremental propensity score interventions](https://mlsanity.com/paper/1704.00211/) (2017)
- [Stable discovery of interpretable subgroups via calibration in causal studies](https://mlsanity.com/paper/2008.10109/) (2020)
- [Confidence sets for persistence diagrams](https://mlsanity.com/paper/1303.7117/) (2013)
- [Causal effects based on distributional distances](https://mlsanity.com/paper/1806.02935/) (2018)
- [Causal Rule Sets for Identifying Subgroups with Enhanced Treatment Effect](https://mlsanity.com/paper/1710.05426/) (2017)
- [A Distance Covariance-based Kernel for Nonlinear Causal Clustering in Heterogeneous Populations](https://mlsanity.com/paper/2106.03480/) (2021)
- [Causal Inference and Mechanism Clustering of A Mixture of Additive Noise Models](https://mlsanity.com/paper/1809.08568/) (2018)
- [Robust Hierarchical Clustering](https://mlsanity.com/paper/1401.0247/) (2014)
- [Discovering Reliable Causal Rules](https://mlsanity.com/paper/2009.02728/) (2020)
- [Causal K-Means Clustering](https://mlsanity.com/paper/2405.03083/) (2024)
- [DeBaCl: A Python Package for Interactive DEnsity-BAsed CLustering](https://mlsanity.com/paper/1307.8136/) (2013)
- [Hierarchical clustering: visualization, feature importance and model selection](https://mlsanity.com/paper/2112.01372/) (2021)
- [A framework for causal segmentation analysis with machine learning in large-scale digital experiments](https://mlsanity.com/paper/2111.01223/) (2021)

## Built on by (most cited first, 6 of 6)

- [Learning Reconfigurable Representations for Multimodal Federated Learning with Missing Data](https://mlsanity.com/paper/2510.22880/) (2025)
- [Interpretable Clustering with Adaptive Heterogeneous Causal Structure Learning in Mixed Observational Data](https://mlsanity.com/paper/2509.04415/) (2025)
- [M-learner:A Flexible And Powerful Framework To Study Heterogeneous Treatment Effect In Mediation Model](https://mlsanity.com/paper/2505.17917/) (2025)
- [Bayesian Supervised Causal Clustering](https://mlsanity.com/paper/2603.05288/) (2026)
- [CaSPECT: Discovering Causally Homogeneous Subgroups via Directed Spectral Clustering](https://mlsanity.com/paper/2607.03364/) (2026)
- [Analysis of Public Schools Educational Performance Based on Causal Models and Hierarchical Clustering](https://mlsanity.com/paper/2607.14124/) (2026)

## Abstract (arXiv)

Understanding treatment effect heterogeneity is vital for scientific and policy research. However, identifying and evaluating heterogeneous treatment effects pose significant challenges due to the typically unknown subgroup structure. Recently, a novel approach, causal k-means clustering, has emerged to assess heterogeneity of treatment effect by applying the k-means algorithm to unknown counterfactual regression functions. In this paper, we expand upon this framework by integrating hierarchical and density-based clustering algorithms. We propose plug-in estimators that are simple and readily implementable using off-the-shelf algorithms. Unlike k-means clustering, which requires the margin condition, our proposed estimators do not rely on strong structural assumptions on the outcome process. We go on to study their rate of convergence, and show that under the minimal regularity conditions, the additional cost of causal clustering is essentially the estimation error of the outcome regression functions. Our findings significantly extend the capabilities of the causal clustering framework, thereby contributing to the progression of methodologies for identifying homogeneous subgroups in treatment response, consequently facilitating more nuanced and targeted interventions. The proposed methods also open up new avenues for clustering with generic pseudo-outcomes. We explore finite sample properties via simulation, and illustrate the proposed methods in voting and employment projection datasets.