Hdr de Slawomir Staworko

Symbolic Inference Methods for Databases

This dissertation is a summary of a line of research, that I was actively involved in, on learning in databases from examples. This research focused on traditional as well as novel database models and languages for querying, transforming, and describing the schema of a database. In case of schemas our contributions involve proposing an original languages for the emerging data models of Unordered XML and RDF. We have studied learning from examples of schemas for Unordered XML, schemas for RDF, twig queries for XML, join queries for relational databases, and XML transformations defined with a novel model of tree-to-word transducers. Investigating learnability of the proposed languages required us to examine closely a number of their fundamental properties, often of independent interest, including normal forms, minimization, containment and equivalence, consistency of a set of examples, and finite characterizability. Good understanding of these properties allowed us to devise learning algorithms that explore a possibly large search space with the help of a diligently designed set of generalization operations in search of an appropriate solution. Learning (or inference) is a problem that has two parameters: the precise class of languages we wish to infer and the type of input that the user can provide. We focused on the setting where the user input consists of positive examples i.e., elements that belong to the goal language, and negative examples i.e., elements that do not belong to the goal language. In general using both negative and positive examples allows to learn richer classes of goal languages than using positive examples alone. However, using negative examples is often difficult because together with positive examples they may cause the search space to take a very complex shape and its exploration may turn out to be computationally challenging.

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