Learning Tuple Probabilities

Learning the parameters of complex probabilistic-relationalmodels from labeled training data is a standard technique inmachine learning, which has been intensively studied in thesubfield of Statistical Relational Learning (SRL), but—sofar—this is still an under-investigated topic in the contextof Probabilistic Databases (PDBs). In this paper, we fo-cus on learning the probability values of base tuples in aPDB from labeled lineage formulas. The resulting learningproblem can be viewed as the inverse problem to confidencecomputations in PDBs: given a set of labeled query answers,learn the probability values of the base tuples, such thatthe marginal probabilities of the query answers again yieldin the assigned probability labels. We analyze the learn-ing problem from a theoretical perspective, cast it into anoptimization problem, and provide an algorithm based onstochastic gradient descent. Finally, we conclude by an ex-perimental evaluation on three real-world and one syntheticdataset, thus comparing our approach to various techniquesfrom SRL, reasoning in information extraction, and opti-mization.