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SUMMARY:Root Cause Discovery via Permutations and Cholesky Decomposition -
  Jinzhou Li (National University of Singapore)
DTSTART:20260304T111500Z
DTEND:20260304T120000Z
UID:TALK244393@talks.cam.ac.uk
DESCRIPTION:Although the statistical literature on causality has largely f
 ocused on forward causal problems concerning the effects of causes\, rever
 se causal questions about identifying the causes of effects are equally im
 portant. In this talk\, we discuss one such reverse causal question\, know
 n as root cause discovery\, which aims to identify the root cause of an ob
 served effect. This work is motivated by the problem of identifying the di
 sease-causing gene (i.e.\, the root cause) in a patient affected by a mono
 genic disorder\, using the gene expression data of healthy individuals as 
 reference. We consider a linear structural equation model with unknown cau
 sal ordering and model the root cause as the intervened variable. We first
  show that simply comparing marginal squared z-scores cannot identify the 
 root cause in general. We then prove\, without additional assumptions\, th
 at the root cause is identifiable even when the causal ordering is not. Tw
 o key ingredients of this identifiability result are the use of permutatio
 ns and Cholesky decomposition\, which allow us to exploit an invariant pro
 perty across different permutations to discover the root cause. Furthermor
 e\, we characterize permutations that yield the correct root cause and\, b
 ased on this\, propose a valid method for root cause discovery. We also ad
 apt this approach to high-dimensional settings. Finally\, we evaluate the 
 performance of our methods through simulations and apply the high-dimensio
 nal method to identify disease-causing genes in the gene expression datase
 t that motivates this work.
LOCATION:Seminar Room 1\, Newton Institute
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