A0618
Title: Root cause discovery via permutations and Cholesky decomposition
Authors: Jinzhou Li - Stanford University (United States) [presenting]
Benjamin Chu - University of California, Los Angeles (United States)
Julien Gagneur - LMU Munich University (Germany)
Marloes Maathuis - ETH Zurich (Switzerland)
Abstract: The motivation is from the following problem: Can the disease-causing gene in a patient affected by a monogenic disorder be identified? This problem is an instance of root cause discovery. In particular, the aim is to identify the intervened variable in one interventional sample using a set of observational samples as reference. A linear structural equation model is considered where the causal ordering is unknown. It begins by examining a simple method that uses squared z-scores and characterizing the conditions under which this method succeeds and fails, showing that it generally cannot identify the root cause. It is then proven, 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 allows exploiting an invariant property across different permutations to discover the root cause. Furthermore, permutations that yield the correct root cause are characterized and, based on this, a valid method for root cause discovery is proposed. This approach is also adapted to high-dimensional settings. Finally, the performance of the methods is evaluated through simulations, and the high-dimensional method is applied to discover disease-causing genes in the gene expression dataset that motivates this work.
