Inferring cause from effects using observational data is a major challenge in many experimental sciences. Based on the principle of "independence of cause and mechanism", the causal links between multivariate variables that relate to each other through mechanism such as linear transformations or deterministic linear dynamical systems can be inferred. Noise contamination of the observed variables can however deteriorate the performance of these approaches. The goal of this research is to study how noise can be estimated in these models and how they can help improve the performance of causal inference.