Optimizing mpf queries

Abstract

Managing uncertain data using probabilistic frameworks has attracted much interest lately in the database literature, and a central computational challenge is probabilistic inference. This paper presents a broad class of aggregate queries, called MPF queries, inspired by the literature on probabilistic inference in statistics and machine learning. An MPF (Marginalize a Product Function) query is an aggregate query over a stylized join of several relations. In probabilistic inference, this join corresponds to taking the product of several probability distributions, while the aggregate operation corresponds to marginalization. Probabilistic inference can be expressed directly as MPF queries in a relational setting, and therefore, by optimizing evaluation of MPF queries, we provide scalable support for probabilistic inference in database systems. To optimize MPF queries, we build on ideas from database query optimization as well as traditional algorithms such as Variable Elimination and Belief Propagation from the probabilistic inference literature. Although our main motivation for introducing MPF queries is to support easy expression and efficient evaluation of probabilistic inference in a DBMS, we observe that this class of queries is very useful for a range of decision support tasks. We present and optimize MPF queries in a general form where arbitrary functions (i.e., other than probability distributions) are handled, and demonstrate their value for decision support applications through a number of illustrative and natural examples.