# LILI clustering algorithm: Limit Inferior Leaf Interval Integrated into Causal Forest for Causal Interference

arXiv: https://arxiv.org/abs/2507.03271 · HTML: https://mlsanity.com/paper/2507.03271/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Causal Embeddings for Recommendation](https://mlsanity.com/paper/1706.07639/) (2017)
- [Clicks can be Cheating: Counterfactual Recommendation for Mitigating Clickbait Issue](https://mlsanity.com/paper/2009.09945/) (2020)
- [Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression](https://mlsanity.com/paper/2005.14458/) (2020)
- [DoubleML -- An Object-Oriented Implementation of Double Machine Learning in Python](https://mlsanity.com/paper/2104.03220/) (2021)
- [Causal Inference for Recommendation: Foundations, Methods and Applications](https://mlsanity.com/paper/2301.04016/) (2023)
- [Matching Algorithms for Causal Inference with Multiple Treatments](https://mlsanity.com/paper/1809.00269/) (2018)

## Abstract (arXiv)

Causal forest methods are powerful tools in causal inference. Similar to traditional random forest in machine learning, causal forest independently considers each causal tree. However, this independence consideration increases the likelihood that classification errors in one tree are repeated in others, potentially leading to significant bias in causal e ect estimation. In this paper, we propose a novel approach that establishes connections between causal trees through the Limit Inferior Leaf Interval (LILI) clustering algorithm. LILIs are constructed based on the leaves of all causal trees, emphasizing the similarity of dataset confounders. When two instances with di erent treatments are grouped into the same leaf across a su cient number of causal trees, they are treated as counterfactual outcomes of each other. Through this clustering mechanism, LILI clustering reduces bias present in traditional causal tree methods and enhances the prediction accuracy for the average treatment e ect (ATE). By integrating LILIs into a causal forest, we develop an e cient causal inference method. Moreover, we explore several key properties of LILI by relating it to the concepts of limit inferior and limit superior in the set theory. Theoretical analysis rigorously proves the convergence of the estimated ATE using LILI clustering. Empirically, extensive comparative experiments demonstrate the superior performance of LILI clustering.