Answering Queries from Statistics and Probabilistic Views∗
Answering Queries from Statistics and Probabilistic Views∗ Nilesh Dalvi Dan Suciu University of Washington, Seattle, WA, USA 1 Introduction paper we will assume the Local As View (LAV) data integration paradigm [17, 16], which consists of defin- Systems integrating dozens of databases, in the scien- ing a global mediated schema R¯, then expressing each tific domain or in a large corporation, need to cope local source i as a view vi(R¯) over the global schema. with a wide variety of imprecisions, such as: different Users are allowed to ask queries over the global, me- representations of the same object in different sources; diated schema, q(R¯), however the data is given as in- imperfect and noisy schema alignments; contradictory stances J1; : : : ; Jm of the local data sources. In our information across sources; constraint violations; or in- model all instances are probabilistic, both the local sufficient evidence to answer a given query. If standard instances and the global instance. Statistics are given query semantics were applied to such data, all but the explicitly over the global schema R¯, and the probabil- most trivial queries will return an empty answer. ities are given explicitly over the local sources, hence We believe that probabilistic databases are the right over the views. We make the Open World Assumption paradigm to model all types of imprecisions in a uni- throughout the paper. form and principled way. A probabilistic database is a probability distribution on all instances [5, 4, 15, 1.1 Example: Using Statistics 12, 11, 8]. Their early motivation was to model im- precisions at the tuple level: tuples are not known Suppose we integrate two sources, one show- with certainty to belong to the database, or represent ing which employee works for what depart- noisy measurements, etc.
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