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Li, J.* ; Chu, B.B.* ; Scheller, I.* ; Gagneur, J. ; Maathuis, M.H.*

Root cause discovery via permutations and Cholesky decomposition.

J. R. Stat. Soc. Ser. B-Stat. Methodol., DOI: 10.1093/jrsssb/qkaf066 (2025)
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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. Specifically, 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 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 our methods through simulations and apply the high-dimensional method to discover disease-causing genes in the gene expression dataset that motivates this work.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Minimum Degree Algorithm ; Root (linguistics) ; Root Cause Analysis; Interventions; Inference; Selection; Model
Language english
Publication Year 2025
HGF-reported in Year 2025
ISSN (print) / ISBN 1369-7412
e-ISSN 1467-9868
Journal Journal of the Royal Statistical Society. Series B: Statistical Methodology
Publisher Oxford University Press
Publishing Place Great Clarendon St, Oxford Ox2 6dp, England
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)
POF-Topic(s) 30205 - Bioengineering and Digital Health
Research field(s) Enabling and Novel Technologies
PSP Element(s) G-503800-001
Grants
IT Infrastructure for Computational Molecular Medicine
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
Stanford Biomedical Informatics National Library of Medicine (NLM) Training
Swiss National Science Foundation (SNSF)
DOI 10.1093/jrsssb/qkaf066
WOS ID 001594567100001
Erfassungsdatum 2025-10-21
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