CausalHighDim · Causal Statistical Inference from High-Dimensional Data

Statistical causal structure learning tackles the following problem: given iid observational data from a joint distribution, we estimate the underlying causal graph. This graph contains a directed arrow from each variable to its direct effects and is assumed to be acyclic. We propose to develop methods and mathematical theory for high-dimensional applications, where the number of variables is much larger than the number of samples.Independence-based methods like the PC algorithm can discover causal structures only up to Markov equivalence classes, that is some arrows remain undirected. And their consistency relies on strong faithfulness, which has been shown to be a restrictive condition. We propose to exploit structural equation models (SEMs) instead. They assume each variable to be a function of its direct causes and some noise variable. For certain restrictions (e.g. non-linear functions and additive noise) we obtain full identifiability