Parameter Learning in Probabilistic Databases: A Least Squares ApproachBernd Gutmann; Angelika Kimmig; Kristian Kersting; Luc De Raedt
In: Walter Daelemans; Bart Goethals; Katharina Morik (Hrsg.). Machine Learning and Knowledge Discovery in Databases, European Conference, Proceedings. European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD-2008), September 15-19, Antwerp, Belgium, Pages 473-488, Lecture Notes in Computer Science, Vol. 5211, Springer, 2008.
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 examples as well as on unseen examples. Assuming Gaussian error terms on the observed success probabilities, this naturally leads to a least squares optimization problem. Our approach, called LeProbLog, is able to learn both from queries and from proofs and even from both simultaneously. This makes it flexible and allows faster training in domains where the proofs are available. Experiments on real world data show the usefulness and effectiveness of this least squares calibration of probabilistic databases.