This paper introduces a regression method, called Privileged Information-based Conditional Structured Output Regression Forest (PI-CSORF) for facial point detection. In order to train Regression Forest more efficiently, the method utilizes both privileged information, that is available only during training such as head pose or gender, and shape constraints on the location of the facial points. We propose to select the test functions at some randomly chosen internal tree nodes according to the information gain calculated on the privileged information. In this way the training patches arrive at leaves tend to have low variance both in terms of their displacements in relation to the facial points and in terms of the privileged information. At each leaf node, we learn three models: first, a probabilistic model of the pdf of the privileged information; second, a probabilistic regression model for the locations of the facial points; and third, shape models that model the interdependencies of the locations of neighbouring facial points in a predefined structure graph. Both of the latter two are conditioned on the privileged information. During testing, the marginal probability of the privileged information is estimated and the facial point locations are localized using the appropriate conditional regression and shape models. The proposed method is validated and compared with very recent methods, especially that use Regression Forests, on datasets recorded in controlled and uncontrolled environments, namely the BioID, the Labelled Faces in the Wild, the Labelled Face Parts in the Wild and the Annotated Facial Landmarks in the Wild.