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Causal Statistical Inference from High-Dimensional Data (CausalHighDim)
Date du début: 1 mars 2013, Date de fin: 28 févr. 2015 PROJET  TERMINÉ 

"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; that is, given an observational distribution, we can recover the underlying causal graph, even without requiring faithfulness. On low-dimensional data sets, SEM-based methods already outperform competing methods like PC. However, they are not applicable to high-dimensional problems yet. One of the main goals of this research proposal is to develop new SEM-based methodology for high-dimensional applications and provide a theoretical analysis.In many applications, data are often collected under different environmental conditions. It is expected that the causal dependencies of a plant's genes, for example, behave differently under stress conditions like drought. Modeling these mechanism changes and exploiting them for causal structure learning is the second main goal of the research proposal. To the best of our knowledge, there is currently no methodology available for these tasks.We will apply the developed methodology to biological systems. The research is closely linked to the interdisciplinary project ""InfectX""."