This paper studies the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is hardly sustainable in large-scale problems and devising efficient alternatives is a challenge. In this work, we investigate if and how Gaussian process regression directly applied to classification labels can be used to tackle this question. While in this case training is remarkably faster, predictions need to be calibrated for classification and uncertainty estimation. To this aim, we propose a novel regression approach where the labels are obtained through the interpretation of classification labels as the coefficients of a degenerate Dirichlet distribution. Extensive experimental results show that the proposed approach provides essentially the same accuracy and uncertainty quantification as Gaussian process classification while requiring only a fraction of computational resources.