Learning Causal Graphs via Monotone Triangular Transport Maps
This addresses the problem of causal discovery for researchers and practitioners in fields requiring causal inference, offering a more flexible approach, though it appears incremental as it builds on existing transport map methods.
The paper tackles causal structure learning from data by developing a method based on optimal transport and monotone triangular transport maps that works without assumptions on noise distributions and handles latent variables. The approach achieves competitive performance with state-of-the-art methods on synthetic and real-world datasets.
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. This allows us to uniquely recover the causal graph under additional identifiability and structural assumptions, such as additive noise or post-nonlinear models. We provide experimental results to compare the proposed approach with the state of the art on both synthetic and real-world datasets.