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We propose a new algorithm to detect facial points in frontal and near-frontal face images. It combines a regression-based approach with a probabilistic graphical model-based face shape model that restricts the search to anthropomorphically consistent regions. While most regression-based approaches perform a sequential approximation of the target location, our algorithm detects the target location by aggregating the estimates obtained from stochastically selected local appearance information into a single robust prediction. The underlying assumption is that by aggregating the different estimates, their errors will cancel out as long as the regressor inputs are uncorrelated. Once this new perspective is adopted, the problem is reformulated as how to optimally select the test locations over which the regressors are evaluated. We propose to extend the regression-based model to provide a quality measure of each prediction, and use the shape model to restrict and correct the sampling region. Our approach combines the low computational cost typical of regression-based approaches with the robustness of exhaustive-search approaches. The proposed algorithm was tested on over 7,500 images from five databases. Results showed significant improvement over the current state of the art.