Supervising topic models with Gaussian processes.

•We propose the first model that can supervise Latent Dirichlet Allocation (LDA) by Gaussian Processes (GPs).•LDA and GP are jointly trained by a novel variational inference algorithm that adopts ideas form Deep GPs.•Differently from Supervised LDA (sLDA), our model learns non-linear mappings from topic activations to document classes.•By virtue of this non-linearity, our model outperforms s LDA, as well as a disjointly trained cascade of LDA and GP in three real-world data sets from two different domains.