# Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model

arXiv: https://arxiv.org/abs/2205.13085 · HTML: https://mlsanity.com/paper/2205.13085/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 50 references that are in the map.
- First posted on arXiv 25 May 2022.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Causal structure based root cause analysis of outliers](https://mlsanity.com/paper/1912.02724/) (2019)
- [Why did the distribution change?](https://mlsanity.com/paper/2102.13384/) (2021)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [Causal Inference via Kernel Deviance Measures](https://mlsanity.com/paper/1804.04622/) (2018)
- [Identifying Patient-Specific Root Causes of Disease](https://mlsanity.com/paper/2205.11627/) (2022)
- [Justifying Information-Geometric Causal Inference](https://mlsanity.com/paper/1402.2499/) (2014)

## Built on by (most cited first, 30 of 38)

- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Modeling Causal Mechanisms with Diffusion Models for Interventional and Counterfactual Queries](https://mlsanity.com/paper/2302.00860/) (2023)
- [Root Cause Analysis of Outliers with Missing Structural Knowledge](https://mlsanity.com/paper/2406.05014/) (2024)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Why Do Probabilistic Clinical Models Fail To Transport Between Sites?](https://mlsanity.com/paper/2311.04787/) (2023)
- [Counterfactual Formulation of Patient-Specific Root Causes of Disease](https://mlsanity.com/paper/2305.17574/) (2023)
- [Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testing](https://mlsanity.com/paper/2301.12930/) (2023)
- [Heteroscedastic Causal Structure Learning](https://mlsanity.com/paper/2307.07973/) (2023)
- [A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery](https://mlsanity.com/paper/2410.06407/) (2024)
- [Sample-Specific Root Causal Inference with Latent Variables](https://mlsanity.com/paper/2210.15340/) (2022)
- [Robust Estimation of Causal Heteroscedastic Noise Models](https://mlsanity.com/paper/2312.10102/) (2023)
- [Distinguishing Cause from Effect with Causal Velocity Models](https://mlsanity.com/paper/2502.05122/) (2025)
- [Structural restrictions in local causal discovery: identifying direct causes of a target variable](https://mlsanity.com/paper/2307.16048/) (2023)
- [Order-based Structure Learning with Normalizing Flows](https://mlsanity.com/paper/2308.07480/) (2023)
- [Multi-Domain Causal Discovery in Bijective Causal Models](https://mlsanity.com/paper/2504.21261/) (2025)
- [Causal Discovery via Quantile Partial Effect](https://mlsanity.com/paper/2509.12981/) (2025)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Assessing the overall and partial causal well-specification of nonlinear additive noise models](https://mlsanity.com/paper/2310.16502/) (2023)
- [Unsupervised Discovery of Clinical Disease Signatures Using Probabilistic Independence](https://mlsanity.com/paper/2402.05802/) (2024)
- [ProRCA: A Causal Python Package for Actionable Root Cause Analysis in Real-world Business Scenarios](https://mlsanity.com/paper/2503.01475/) (2025)
- [Flow-based Generative Modeling of Potential Outcomes and Counterfactuals](https://mlsanity.com/paper/2505.16051/) (2025)
- [Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises](https://mlsanity.com/paper/2506.17065/) (2025)
- [Counterfactual-based Root Cause Analysis for Dynamical Systems](https://mlsanity.com/paper/2406.08106/) (2024)
- [DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms](https://mlsanity.com/paper/2607.11510/) (2026)
- [Skewness-Robust Causal Discovery in Location-Scale Noise Models](https://mlsanity.com/paper/2511.14441/) (2025)
- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)

## Abstract (arXiv)

Complex diseases are caused by a multitude of factors that may differ between patients even within the same diagnostic category. A few underlying root causes may nevertheless initiate the development of disease within each patient. We therefore focus on identifying patient-specific root causes of disease, which we equate to the sample-specific predictivity of the exogenous error terms in a structural equation model. We generalize from the linear setting to the heteroscedastic noise model where Y = m(X) + varepsilonσ(X) with non-linear functions m(X) and σ(X) representing the conditional mean and mean absolute deviation, respectively. This model preserves identifiability but introduces non-trivial challenges that require a customized algorithm called Generalized Root Causal Inference (GRCI) to extract the error terms correctly. GRCI recovers patient-specific root causes more accurately than existing alternatives.