Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this uncertainty to a desired level of fidelity. Our approach allows the efficient evaluation of arbitrary queries over probabilistic databases with arbitrary dependencies expressed by graphical models with structure that changes during inference. MCMC sampling provides efficiency by hypothesizing modifications to possible worlds rather than generating entire worlds from scratch. Queries are then run over the portions of the world that change, avoiding the onerous cost of running full queries over each sampled world. A significant innovation of this work is the connection between MCMC sampling and materialized view maintenance techniques: we find empirically that using view maintenance techniques is several orders of magnitude faster than naively querying each sampled world. We also demonstrate our system's ability to answer relational queries with aggregation, and demonstrate additional scalability through the use of parallelization.
Because early theoretical work on incomplete data focuses largely on algebras and representation systems (e.g., @cite_29 @cite_11 ), it was only natural to extend this line of thinking to probabilities @cite_8 @cite_25 @cite_2 @cite_16 @cite_24 benjelloun06uldbs . However, this extension is quite difficult since the probabilities in query results must include expressions derived from the confidence values originally embedded in the database. Systems meeting these theoretical conditions must overcome a set of challenges that are often satisfied at the expense of modeling-power or understandability.
@cite_8 @cite_29 @cite_24 @cite_2 @cite_16 @cite_25 @cite_11
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We consider the problem of answering queries from databases that may be incomplete. A database is incomplete if some tuples may be missing from some relations, and only a part of each relation is known to be complete. This problem arises in several contexts. For example, systems that provide access to multiple heterogeneous information sources often encounter incomplete sources. The question we address is to determine whether the answer to a specific given query is complete even when the database is incomplete. We present a novel sound and complete algorithm for the answer-completeness problem by relating it to the problem of independence of queries from updates. We also show an important case of the independence problem (and therefore ofthe answer-completeness problem) that can be decided in polynomial time, whereas the best known algorithm for this case is exponential. This case involves updates that are described using a conjunction of comparison predicates. We also describe an algorithm that determines whether the answer to the query is complete in the current state of the database. Finally, we show that our ‘treatment extends naturally to partiallyincorrect databases. Permission to copy without fee all or part of this material is granted provided that the copies aTe not made OT distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, OT to republish, requirea a fee and or special permission from the Endowment. Proceedings of the 22nd VLDB Conference Mumbai(Bombay), India, 1996 It is often desirable to represent in a database, entities whose properties cannot be deterministically classified. The authors develop a data model that includes probabilities associated with the values of the attributes. The notion of missing probabilities is introduced for partially specified probability distributions. This model offers a richer descriptive language allowing the database to more accurately reflect the uncertain real world. Probabilistic analogs to the basic relational operators are defined and their correctness is studied. A set of operators that have no counterpart in conventional relational systems is presented. > We discuss, compare and relate some old and some new models for incomplete and probabilistic databases. We characterize the expressive power of c-tables over infinite domains and we introduce a new kind of result, algebraic completion, for studying less expressive models. By viewing probabilistic models as incompleteness models with additional probability information, we define completeness and closure under query languages of general probabilistic database models and we introduce a new such model, probabilistic c-tables, that is shown to be complete and closed under the relational algebra. Incomplete information arises naturally in numerous data management applications. Recently, several researchers have studied query processing in the context of incomplete information. Most work has combined the syntax of a traditional query language like relational algebra with a nonstandard semantics such as certain or ranked possible answers. There are now also languages with special features to deal with uncertainty. However, to the standards of the data management community, to date no language proposal has been made that can be considered a natural analog to SQL or relational algebra for the case of incomplete information. In this paper we propose such a language, World-set Algebra, which satisfies the robustness criteria and analogies to relational algebra that we expect. The language supports the contemplation on alternatives and can thus map from a complete database to an incomplete one comprising several possible worlds. We show that World-set Algebra is conservative over relational algebra in the sense that any query that maps from a complete database to a complete database (a complete-to-complete query) is equivalent to a relational algebra query. Moreover, we give an efficient algorithm for effecting this translation. We then study algebraic query optimization of such queries. We argue that query languages with explicit constructs for handling uncertainty allow for the more natural and simple expression of many real-world decision support queries. The results of this paper not only suggest a language for specifying queries in this way, but also allow for their efficient evaluation in any relational database management system.