Many noise models do not faithfully reflect the noise processes introduced during data collection in many real-world applications. In particular, we argue that a type of noise referred to as sparse noise is quite commonly found in many applications and many existing works have been proposed to model such sparse noise. However, all the existing works only focus on unsupervised learning without considering the supervised information, i.e., label information. In this paper, we consider how to model and handle sparse noise in the context of embedding high-dimensional data under a probabilistic formulation for supervised learning. We propose a supervised probabilistic robust embedding (SPRE) model in which data are corrupted either by sparse noise or by a combination of Gaussian and sparse noises. By using the Laplace distribution as a prior to model sparse noise, we devise a twofold variational EM learning algorithm in which the update of model parameters has analytical solution. We report some classification experiments to compare SPRE with several related models.
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