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We study the problem of causal structure learning from data using optimaltransport (OT). Specifically, we first provide a constraint-based method whichbuilds upon lower-triangular monotone parametric transport maps to designconditional independence tests which are agnostic to the noise distribution. Weprovide an algorithm for causal discovery up to Markov Equivalence with noassumptions on the structural equations/noise distributions, which allows forsettings with latent variables. Our approach also extends to score-based causaldiscovery by providing a novel means for defining scores. This allows us touniquely recover the causal graph under additional identifiability andstructural assumptions, such as additive noise or post-nonlinear models. Weprovide experimental results to compare the proposed approach with the state ofthe art on both synthetic and real-world datasets.

Learning Causal Graphs via Monotone Triangular Transport Maps