TY  - JOUR
AB  - 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.
AU  - Li, J.*
AU  - Chu, B.B.*
AU  - Scheller, I.*
AU  - Gagneur, J.
AU  - Maathuis, M.H.*
C1  - 75812
C2  - 58051
CY  - Great Clarendon St, Oxford Ox2 6dp, England
TI  - Root cause discovery via permutations and Cholesky decomposition.
JO  - J. R. Stat. Soc. Ser. B-Stat. Methodol.
PB  - Oxford Univ Press
PY  - 2025
SN  - 1369-7412
ER  -