Markov logic mixtures of Gaussian processes: Towards machines reading regression data

We propose a novel mixtures of Gaussian processes model in which the gating function is interconnected with a probabilistic logical model, in our case Markov logic networks. In this way, the resulting mixed graphical model, called Markov logic mixtures of Gaussian processes (MLxGP), solves joint Bayesian non-parametric regression and probabilistic relational inference tasks. In turn, MLxGP facilitates novel, interesting tasks such as regression based on logical constraints or drawing probabilistic logical conclusions about regression data, thus putting "machines reading regression data" in reach.