Probabilistic Data Management Project

   We have developed several theories and algorithms to scale databases and inference mechanisms to handle uncertainty.

• PROBVIEW: ProbView was the first probabilistic database system that did not force all users to assume that all the data in a probabilistic database represented independent events. We developed the ProbView data model, and developed a set of relational algebra operations that allowed users to parameterize queries with their knowledge about dependencies (or lack thereof) between events. The ProbView system was built on top of Paradox.
• Temporal Probabilistic (TP) databases: When uncertainty over time is to be considered, there can be a huge amount of uncertainty to manage. The sentence ?Package p will be delivered between 8 am and 5pm? breaks down to thousands of possibilities if we are reasoning on a second by second level. We developed the concept of a tp-relation and extended the relational algebra to handle tp-relations. We also implement TP-databases on top of ODBC. We have developed cost models for TP-data, as well as query optimizers for it.
• Probabilistic XML: We have developed two extensions of XML to handle probabilistic data. The first (PXML) is a Bayesian model of probabilistic XML that extends the relational algebra to handle probabilistic XML. The second (PiXML) is an interval extension of XML to handle probabilities without the ubiquitous independence assumption. It uses a sound and complete calculus for querying such data sources.
• Probabilistic Object Bases: We developed one of the first extensions of object database systems to handle probabilities. We extended the relational algebra to handle probabilistic object bases and developed equivalence results in the algebra. The algebra was implemented on top of ObjectStore. An extension of the algebra to handle probabilistic temporal uncertainty has also been developed.
• Probabilistic Aggregates: We are working on incorporating aggregate operators into all forms of probabilistic databases.
• Probabilistic Logic Programming: We have worked extensively on probabilistic logic programming where we have developed model theories, fixpoint theories proof theories, and query processing algorithms for probabilistic logic programs.