# Detecting Changes in Causal Dependence with Kernels and Copulas

arXiv: https://arxiv.org/abs/2605.05809 · HTML: https://mlsanity.com/paper/2605.05809/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 60 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 21 of 21)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1810.03024/) (2018)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [A Rigorous Theory of Conditional Mean Embeddings](https://mlsanity.com/paper/1912.00671/) (2019)
- [A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data](https://mlsanity.com/paper/1306.4933/) (2013)
- [Causal Structure Discovery from Distributions Arising from Mixtures of DAGs](https://mlsanity.com/paper/2001.11940/) (2020)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [Partial Distance Correlation with Methods for Dissimilarities](https://mlsanity.com/paper/1310.2926/) (2013)
- [Direct Estimation of Differences in Causal Graphs](https://mlsanity.com/paper/1802.05631/) (2018)
- [DRCFS: Doubly Robust Causal Feature Selection](https://mlsanity.com/paper/2306.07024/) (2023)
- [Direct Learning with Guarantees of the Difference DAG Between Structural Equation Models](https://mlsanity.com/paper/1906.12024/) (2019)
- [A Fast Non-parametric Approach for Local Causal Structure Learning](https://mlsanity.com/paper/2111.14969/) (2021)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [Double Machine Learning Based Structure Identification from Temporal Data](https://mlsanity.com/paper/2311.06012/) (2023)
- [Causal Change Point Detection and Localization](https://mlsanity.com/paper/2403.12677/) (2024)
- [Identifying General Mechanism Shifts in Linear Causal Representations](https://mlsanity.com/paper/2410.24059/) (2024)
- [Kernel-based Partial Permutation Test for Detecting Heterogeneous Functional Relationship](https://mlsanity.com/paper/2110.15406/) (2021)
- [Nonparametric data segmentation in multivariate time series via joint characteristic functions](https://mlsanity.com/paper/2305.07581/) (2023)
- [Causal Discovery-Driven Change Point Detection in Time Series](https://mlsanity.com/paper/2407.07290/) (2024)
- [Quickest Causal Change Point Detection by Adaptive Intervention](https://mlsanity.com/paper/2506.07760/) (2025)

## Abstract (arXiv)

We propose a framework for determining whether the causal dependence of an outcome Y on a covariate X changes at a given time point, given confounders boldsymbolZ. For instance, in financial markets, the effect of a market indicator on asset returns may causally change over time. While many existing measures of association can be used to detect changes in joint and marginal distributions, in the absence of strong assumptions on the data generating process none are suitable for detecting changes in the causal mechanism or in the strength of causal relationship. In this work we approach the problem from a fully non-parametric perspective, and treat the causal mechanism as well as the distribution of the data as unknown. We introduce a quantity based on the integrated difference between kernel mean embeddings of certain conditionals copula, which is provably equal to zero if the causal dependence does not change and strictly positive else. A near-linear time estimator for the quantity is proposed, with rates of convergence explicitly spelled out. Extensive experiments demonstrate that the proposed statistic achieves high accuracy on multiple synthetic and real-world datasets. We additionally show how the proposed statistic can be used for change point detection when the goal is to detect changes in causal dependence occurring at an unknown times.