# Root cause discovery via permutations and Cholesky decomposition

arXiv: https://arxiv.org/abs/2410.12151 · HTML: https://mlsanity.com/paper/2410.12151/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2024.

## Built on by (most cited first, 11 of 11)

- [Root Cause Analysis of Outliers in Unknown Cyclic Graphs](https://mlsanity.com/paper/2510.06995/) (2025)
- [Graph-Free Root Cause Analysis](https://mlsanity.com/paper/2601.21359/) (2026)
- [Toward Universal Laws of Outlier Propagation](https://mlsanity.com/paper/2502.08593/) (2025)
- [Root Cause Analysis of Measurement and Mechanistic Anomalies](https://mlsanity.com/paper/2601.23026/) (2026)
- [PRIM: Meta-Learned Bayesian Root Cause Analysis](https://mlsanity.com/paper/2605.08786/) (2026)
- [ORCA: An End-to-End Interactive Copilot for Optimized Root Cause Analysis](https://mlsanity.com/paper/2605.27022/) (2026)
- [Formalizing and falsifying causal pathways of rare events](https://mlsanity.com/paper/2605.31254/) (2026)
- [StableRCA: Robust Graph-Agnostic Mechanism-Level Root Cause Analysis](https://mlsanity.com/paper/2606.05636/) (2026)
- [Graphical Causal Reasoning for Root Cause Analysis in Cloud Networks](https://mlsanity.com/paper/2606.13532/) (2026)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)
- [Where Root Cause Analysis Fails: A Retrieval-Reranking Decomposition](https://mlsanity.com/paper/2609.36686/) (2026)

## Abstract (arXiv)

This work is motivated by the following problem: Can we identify the disease-causing gene in a patient affected by a monogenic disorder? This problem is an instance of root cause discovery. In particular, we aim to identify the intervened variable in one interventional sample using a set of observational samples as reference. We consider a linear structural equation model where the causal ordering is unknown. We begin by examining a simple method that uses squared z-scores and characterize the conditions under which this method succeeds and fails, showing that it generally cannot identify the root cause. We then prove, without additional assumptions, that the root cause is identifiable even if the causal ordering is not. Two key ingredients of this identifiability result are the use of permutations and the Cholesky decomposition, which allow us to exploit an invariant property across different permutations to discover the root cause. Furthermore, we characterize permutations that yield the correct root cause and, based on this, propose a valid method for root cause discovery. We also adapt this approach to high-dimensional settings. Finally, we evaluate the performance of our methods through simulations and apply the high-dimensional method to discover disease-causing genes in the gene expression dataset that motivates this work.