Parameter Learning in Probabilistic Databases: A Least Squares Approach

Probabilistic databases compute the success probabilities of queries. We introduce the problem of learning the parameters of the probabilistic database ProbLog. Given the observed success probabilities of a set of queries, we compute the probabilities attached to facts that have a low approximation error on the training data as well as on unseen examples. Assuming Gaussian error terms on the observed success probabilities, this naturally leads to a least squares optimization problem. Experiments on real world data show the usefulness and effectiveness of this least squares calibration of probabilistic databases.