The dramatic growth in the number of application domains that naturally generate probabilistic, uncertain data has resulted in a need for efficiently supporting complex querying and decision-making over such data. In this paper, we present a unified approach to ranking and top-k query processing in probabilistic databases by viewing it as a multi-criteria optimization problem, and by deriving a set of features that capture the key properties of a probabilistic dataset that dictate the ranked result. We contend that a single, specific ranking function may not suffice for probabilistic databases, and we instead propose two parameterized ranking functions, called PRF-w and PRF-e, that generalize or can approximate many of the previously proposed ranking functions. We present novel generating functions-based algorithms for efficiently ranking large datasets according to these ranking functions, even if the datasets exhibit complex correlations modeled using probabilistic and xor trees or Markov networks. We further propose that the parameters of the ranking function be learned from user preferences, and we develop an approach to learn those parameters. Finally, we present a comprehensive experimental study that illustrates the effectiveness of our parameterized ranking functions, especially PRF-e, at approximating other ranking functions and the scalability of our proposed algorithms for exact or approximate ranking.
There has also been work on top-k query processing in probabilistic databases where the ranking is by the result tuple probabilities (i.e., probability and score are identical) @cite_22 . The main challenge in that work is efficient computation of the probabilities, whereas we assume that the probability and score are either given or can be computed easily.
@cite_22
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When dealing with massive quantities of data, top-k queries are a powerful technique for returning only the k most relevant tuples for inspection, based on a scoring function. The problem of efficiently answering such ranking queries has been studied and analyzed extensively within traditional database settings. The importance of the top-k is perhaps even greater in probabilistic databases, where a relation can encode exponentially many possible worlds. There have been several recent attempts to propose definitions and algorithms for ranking queries over probabilistic data. However, these all lack many of the intuitive properties of a top-k over deterministic data. Specifically, we define a number of fundamental properties, including exact-k, containment, unique-rank, value-invariance, and stability, which are all satisfied by ranking queries on certain data. We argue that all these conditions should also be fulfilled by any reasonable definition for ranking uncertain data. Unfortunately, none of the existing definitions is able to achieve this. To remedy this shortcoming, this work proposes an intuitive new approach of expected rank. This uses the well-founded notion of the expected rank of each tuple across all possible worlds as the basis of the ranking. We are able to prove that, in contrast to all existing approaches, the expected rank satisfies all the required properties for a ranking query. We provide efficient solutions to compute this ranking across the major models of uncertain data, such as attribute-level and tuple-level uncertainty. For an uncertain relation of N tuples, the processing cost is O(N logN)—no worse than simply sorting the relation. In settings where there is a high cost for generating each tuple in turn, we provide pruning techniques based on probabilistic tail bounds that can terminate the search early and guarantee that the top-k has been found. Finally, a comprehensive experimental study confirms the effectiveness of our approach. Top-k processing in uncertain databases is semantically and computationally different from traditional top-k processing. The interplay between score and uncertainty makes traditional techniques inapplicable. We introduce new probabilistic formulations for top-k queries. Our formulations are based on "marriage" of traditional top-k semantics and possible worlds semantics. In the light of these formulations, we construct a framework that encapsulates a state space model and efficient query processing techniques to tackle the challenges of uncertain data settings. We prove that our techniques are optimal in terms of the number of accessed tuples and materialized search states. Our experiments show the efficiency of our techniques under different data distributions with orders of magnitude improvement over naive materialization of possible worlds. A top-k query retrieves the k highest scoring tuples from a data set with respect to a scoring function defined on the attributes of a tuple. The efficient evaluation of top-k queries has been an active research topic and many different instantiations of the problem, in a variety of settings, have been studied. However, techniques developed for conventional, centralized or distributed databases are not directly applicable to highly dynamic environments and on-line applications, like data streams. Recently, techniques supporting top-k queries on data streams have been introduced. Such techniques are restrictive however, as they can only efficiently report top-k answers with respect to a pre-specified (as opposed to ad-hoc) set of queries. In this paper we introduce a novel geometric representation for the top-k query problem that allows us to raise this restriction. Utilizing notions of geometric arrangements, we design and analyze algorithms for incrementally maintaining a data set organized in an arrangement representation under streaming updates. We introduce query evaluation strategies that operate on top of an arrangement data structure that are able to guarantee efficient evaluation for ad-hoc queries. The performance of our core technique is augmented by incorporating tuple pruning strategies, minimizing the number of tuples that need to be stored and manipulated. This results in a main memory indexing technique supporting both efficient incremental updates and the evaluation of ad-hoc top-k queries. A thorough experimental study evaluates the efficiency of the proposed technique. Modern enterprise applications are forced to deal with unreliable, inconsistent and imprecise information. Probabilistic databases can model such data naturally, but SQL query evaluation on probabilistic databases is difficult: previous approaches have either restricted the SQL queries, or computed approximate probabilities, or did not scale, and it was shown recently that precise query evaluation is theoretically hard. In this paper we describe a novel approach, which computes and ranks efficiently the top-k answers to a SQL query on a probabilistic database. The restriction to top-k answers is natural, since imprecisions in the data often lead to a large number of answers of low quality, and users are interested only in the answers with the highest probabilities. The idea in our algorithm is to run in parallel several Monte-Carlo simulations, one for each candidate answer, and approximate each probability only to the extent needed to compute correctly the top-k answers.