Learning Causal Graphs via Monotone Triangular Transport Maps

Understand

We study the problem of causal structure learning from data using optimal transport (OT).

• Specifically, we first provide a constraint-based method which builds upon lower-triangular monotone parametric transport maps to design conditional independence tests which are agnostic to the noise distribution.
• We provide an algorithm for causal discovery up to Markov Equivalence with no assumptions on the structural equations/noise distributions, which allows for settings with latent variables.
• Our approach also extends to score-based causal discovery by providing a novel means for defining scores.