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This paper is about mapping images to continuous output spaces using powerful Bayesian learning techniques. A sparse, semi-supervised Gaussian process regression model (S3GP) is introduced which learns a mapping using only partially labelled training data. We show that sparsity bestows efficiency on the S3GP which requires minimal CPU utilization for real-time operation; the predictions of uncertainty made by the S3GP are more accurate than those of other models leading to considerable performance improvements when combined with a probabilistic filter; and the ability to learn from semi-supervised data simplifies the process of collecting training data. The S3GP uses a mixture of different image features: this is also shown to improve the accuracy and consistency of the mapping. A major application of this work is its use as a gaze tracking system in which images of a human eye are mapped to screen coordinates: in this capacity our approach is efficient, accurate and versatile.