# Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal Kernel Clustering

arXiv: https://arxiv.org/abs/2501.11622 · HTML: https://mlsanity.com/paper/2501.11622/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 63 references that are in the map.
- First posted on arXiv 20 Jan 2025.

## Builds on (most cited first, 29 of 29)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Stable Learning via Sample Reweighting](https://mlsanity.com/paper/1911.12580/) (2019)
- [Stable Prediction with Model Misspecification and Agnostic Distribution Shift](https://mlsanity.com/paper/2001.11713/) (2020)
- [A Survey of Learning Causality with Data: Problems and Methods](https://mlsanity.com/paper/1809.09337/) (2018)
- [Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing](https://mlsanity.com/paper/2211.15728/) (2022)
- [Partial Distance Correlation with Methods for Dissimilarities](https://mlsanity.com/paper/1310.2926/) (2013)
- [Measurement Dependence Inducing Latent Causal Models](https://mlsanity.com/paper/1910.08778/) (2019)
- [Stable Learning via Sparse Variable Independence](https://mlsanity.com/paper/2212.00992/) (2022)
- [High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models](https://mlsanity.com/paper/1804.00778/) (2018)
- [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)
- [The Chi-Square Test of Distance Correlation](https://mlsanity.com/paper/1912.12150/) (2019)
- [A New Framework for Distance and Kernel-based Metrics in High Dimensions](https://mlsanity.com/paper/1909.13469/) (2019)
- [MetaCI: Meta-Learning for Causal Inference in a Heterogeneous Population](https://mlsanity.com/paper/1912.03960/) (2019)
- [Testing mutual independence in high dimension via distance covariance](https://mlsanity.com/paper/1609.09380/) (2016)
- [A Transformational Characterization of Unconditionally Equivalent Bayesian Networks](https://mlsanity.com/paper/2203.00521/) (2022)
- [Multi-label Causal Variable Discovery: Learning Common Causal Variables and Label-specific Causal Variables](https://mlsanity.com/paper/2011.04176/) (2020)
- [CCSL: A Causal Structure Learning Method from Multiple Unknown Environments](https://mlsanity.com/paper/2111.09666/) (2021)
- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [Estimating Heterogeneous Causal Effect of Polysubstance Usage on Drug Overdose from Large-Scale Electronic Health Record](https://mlsanity.com/paper/2105.07224/) (2021)
- [Faster Isomorphism for p-Groups of Class 2 and Exponent p](https://mlsanity.com/paper/2303.15412/) (2023)
- [Multi-granularity Causal Structure Learning](https://mlsanity.com/paper/2312.05549/) (2023)
- [Causal Adjacency Learning for Spatiotemporal Prediction Over Graphs](https://mlsanity.com/paper/2411.16142/) (2024)

## Abstract (arXiv)

Due to the challenge posed by multi-source and heterogeneous data collected from diverse environments, causal relationships among features can exhibit variations influenced by different time spans, regions, or strategies. This diversity makes a single causal model inadequate for accurately representing complex causal relationships in all observational data, a crucial consideration in causal learning. To address this challenge, the nonlinear Causal Kernel Clustering method is introduced for heterogeneous subgroup causal learning, highlighting variations in causal relationships across diverse subgroups. The main component for clustering heterogeneous subgroups lies in the construction of the u-centered sample mapping function with the property of unbiased estimation, which assesses the differences in potential nonlinear causal relationships in various samples and supported by causal identifiability theory. Experimental results indicate that the method performs well in identifying heterogeneous subgroups and enhancing causal learning, leading to a reduction in prediction error.