Causal Discovery with Continuous Additive Noise Models
This addresses the problem of causal inference for researchers and practitioners by enabling full graph identification from observational data, though it is incremental as it builds on existing structural equation models.
The paper tackles the problem of learning causal directed acyclic graphs from observational data, showing that under additive noise models, the graph becomes identifiable, unlike traditional methods that leave edges undirected. It provides algorithms like RESIT, proves correctness in population settings, and includes empirical evaluation.
We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed acyclic graph becomes identifiable from the distribution under mild conditions. This constitutes an interesting alternative to traditional methods that assume faithfulness and identify only the Markov equivalence class of the graph, thus leaving some edges undirected. We provide practical algorithms for finitely many samples, RESIT (Regression with Subsequent Independence Test) and two methods based on an independence score. We prove that RESIT is correct in the population setting and provide an empirical evaluation.