# Why did the distribution change?

arXiv: https://arxiv.org/abs/2102.13384 · HTML: https://mlsanity.com/paper/2102.13384/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 38 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 3 of 3)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)

## Built on by (most cited first, 30 of 37)

- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models](https://mlsanity.com/paper/2206.06821/) (2022)
- [Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model](https://mlsanity.com/paper/2205.13085/) (2022)
- [Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loops](https://mlsanity.com/paper/2303.04038/) (2023)
- [Towards Explaining Distribution Shifts](https://mlsanity.com/paper/2210.10275/) (2022)
- [A Survey on Evaluation of Out-of-Distribution Generalization](https://mlsanity.com/paper/2403.01874/) (2024)
- ["Why did the Model Fail?": Attributing Model Performance Changes to Distribution Shifts](https://mlsanity.com/paper/2210.10769/) (2022)
- [The PetShop Dataset -- Finding Causes of Performance Issues across Microservices](https://mlsanity.com/paper/2311.04806/) (2023)
- [Identifying Patient-Specific Root Causes of Disease](https://mlsanity.com/paper/2205.11627/) (2022)
- [Counterfactual Formulation of Patient-Specific Root Causes of Disease](https://mlsanity.com/paper/2305.17574/) (2023)
- [Sample-Specific Root Causal Inference with Latent Variables](https://mlsanity.com/paper/2210.15340/) (2022)
- [Explanation Shift: How Did the Distribution Shift Impact the Model?](https://mlsanity.com/paper/2303.08081/) (2023)
- [On the Interventional Kullback-Leibler Divergence](https://mlsanity.com/paper/2302.05380/) (2023)
- [Dataflow graphs as complete causal graphs](https://mlsanity.com/paper/2303.09552/) (2023)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [A hierarchical decomposition for explaining ML performance discrepancies](https://mlsanity.com/paper/2402.14254/) (2024)
- [The Thousand Faces of Explainable AI Along the Machine Learning Life Cycle: Industrial Reality and Current State of Research](https://mlsanity.com/paper/2310.07882/) (2023)
- [Explanatory Model Monitoring to Understand the Effects of Feature Shifts on Performance](https://mlsanity.com/paper/2408.13648/) (2024)
- [Identifying General Mechanism Shifts in Linear Causal Representations](https://mlsanity.com/paper/2410.24059/) (2024)
- [Explaining the root causes of unit-level changes](https://mlsanity.com/paper/2206.12986/) (2022)
- [Root Cause Explanation of Outliers under Noisy Mechanisms](https://mlsanity.com/paper/2312.11818/) (2023)
- [Causal Reasoning in Software Quality Assurance: A Systematic Review](https://mlsanity.com/paper/2408.17183/) (2024)
- [On the Fly Detection of Root Causes from Observed Data with Application to IT Systems](https://mlsanity.com/paper/2402.06500/) (2024)
- [Counterfactual-based Root Cause Analysis for Dynamical Systems](https://mlsanity.com/paper/2406.08106/) (2024)
- [Causality-Driven Audits of Model Robustness](https://mlsanity.com/paper/2410.23494/) (2024)
- [Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomena](https://mlsanity.com/paper/2505.06123/) (2025)
- [Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphs](https://mlsanity.com/paper/2510.06735/) (2025)
- [Causal fault localisation in dataflow systems](https://mlsanity.com/paper/2304.11987/) (2023)
- ["Who experiences large model decay and why?" A Hierarchical Framework for Diagnosing Heterogeneous Performance Drift](https://mlsanity.com/paper/2506.00756/) (2025)
- [Order-based Causal Discovery for Multistage Processes](https://mlsanity.com/paper/2607.03971/) (2026)

## Abstract (arXiv)

We describe a formal approach based on graphical causal models to identify the "root causes" of the change in the probability distribution of variables. After factorizing the joint distribution into conditional distributions of each variable, given its parents (the "causal mechanisms"), we attribute the change to changes of these causal mechanisms. This attribution analysis accounts for the fact that mechanisms often change independently and sometimes only some of them change. Through simulations, we study the performance of our distribution change attribution method. We then present a real-world case study identifying the drivers of the difference in the income distribution between men and women.