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This article presents a novel method for causal discovery with generalizedstructural equation models suited for analyzing diverse types of outcomes,including discrete, continuous, and mixed data. Causal discovery often faceschallenges due to unmeasured confounders that hinder the identification ofcausal relationships. The proposed approach addresses this issue by developingtwo peeling algorithms (bottom-up and top-down) to ascertain causalrelationships and valid instruments. This approach first reconstructs asuper-graph to represent ancestral relationships between variables, using apeeling algorithm based on nodewise GLM regressions that exploit relationshipsbetween primary and instrumental variables. Then, it estimates parent-childeffects from the ancestral relationships using another peeling algorithm whiledeconfounding a child's model with information borrowed from its parents'models. The article offers a theoretical analysis of the proposed approach,which establishes conditions for model identifiability and provides statisticalguarantees for accurately discovering parent-child relationships via thepeeling algorithms. Furthermore, the article presents numerical experimentsshowcasing the effectiveness of our approach in comparison to state-of-the-artstructure learning methods without confounders. Lastly, it demonstrates anapplication to Alzheimer's disease (AD), highlighting the utility of the methodin constructing gene-to-gene and gene-to-disease regulatory networks involvingSingle Nucleotide Polymorphisms (SNPs) for healthy and AD subjects.

Causal Discovery with Generalized Linear Models through Peeling Algorithms