Despite the fact, that, in reality facial expressions occur as a result of muscle actions, facial expression models assume an inverse functional relationship, which makes muscles action be the result of facial expressions. Clearly, facial expression should be expressed as a function of muscle action, the other way around as previously suggested. Furthermore, a human facial expression space and the robots actuator space have common features. However, there are also features that the one or the other does not have. This suggests modelling shared and non-shared feature variance separately. To this end we propose Shared Gaussian Process Latent Variable Models (Shared GP-LVM) for models of facial expressions, which assume shared and private features between an input and output space. In this work, we are focusing on the detection of ambiguities within data sets of facial behaviour. We suggest ways of modelling and mapping of facial motion from a representation of human facial expressions to a robot's actuator space. We aim to compensate for ambiguities caused by interference of global with local head motion and the constrained nature of Active Appearance Models, used for tracking.