Aim : Our aim is to develop new methods for causal inference in the context of the Mendelian randomisation (MR) framework.

We are interested in the metabolites data set because we believe it is interesting from both a methodological and biological point of view. MR being an instrumental variable method, it makes strong and untestable assumptions about the effect of genetic variants on measured variables, the 'no pleiotropy' assumption being the most restrictive (Didelez V. et al, 2010).. But one might ask whether it is possible to relax this assumption, and if so with what consequences. When the number of genetic variants and measurement increase, can it be replaced by a different set of assumptions that might be more believable in a biological context. See for example (Silva R and Evans R., 2014) and (Kang et al. 2014) who make assumptions about the strength of the confounders and the number of invalid instruments. To that end, we intend to model all variables together, a method sometimes called "network Mendelian randomisation" (Burgess S. et al, 2014). In particular, we will use recent developments in the fields of matrix recovery and graphical modelling in order to infer the effect of the confounders and identify some of the pleiotropic pathways (Candes E. et al. 2009, Chandrasekaran V., 2011). According to our power analysis, we expect to uncover 60% of the causal links at a false discovery rate of 5 %, and this in the presence of arbitrarily strong confounders. Thanks to simulations for a wide range designs, we have confirmed that our FDRs are well calibrated.