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Linear structural causal models (SCMs) -- in which each observed variable isgenerated by a subset of the other observed variables as well as a subset ofthe exogenous sources -- are pervasive in causal inference and casualdiscovery. However, for the task of causal discovery, existing work almostexclusively focus on the submodel where each observed variable is associatedwith a distinct source with non-zero variance. This results in the restrictionthat no observed variable can deterministically depend on other observedvariables or latent confounders. In this paper, we extend the results onstructure learning by focusing on a subclass of linear SCMs which do not havethis property, i.e., models in which observed variables can be causallyaffected by any subset of the sources, and are allowed to be a deterministicfunction of other observed variables or latent confounders. This allows for amore realistic modeling of influence or information propagation in systems. Wefocus on the task of causal discovery form observational data generated from amember of this subclass. We derive a set of necessary and sufficient conditionsfor unique identifiability of the causal structure. To the best of ourknowledge, this is the first work that gives identifiability results for causaldiscovery under both latent confounding and deterministic relationships.Further, we propose an algorithm for recovering the underlying causal structurewhen the aforementioned conditions are satisfied. We validate our theoreticalresults both on synthetic and real datasets.

Causal Discovery in Linear Structural Causal Models with Deterministic Relations