Top- @math queries allow end-users to focus on the most important (top- @math ) answers amongst those which satisfy the query. In traditional databases, a user defined score function assigns a score value to each tuple and a top- @math query returns @math tuples with the highest score. In uncertain database, top- @math answer depends not only on the scores but also on the membership probabilities of tuples. Several top- @math definitions covering different aspects of score-probability interplay have been proposed in recent past R10,R4,R2,R8 . Most of the existing work in this research field is focused on developing efficient algorithms for answering top- @math queries on static uncertain data. Any change (insertion, deletion of a tuple or change in membership probability, score of a tuple) in underlying data forces re-computation of query answers. Such re-computations are not practical considering the dynamic nature of data in many applications. In this paper, we propose a fully dynamic data structure that uses ranking function @math proposed by R8 under the generally adopted model of @math -relations R11 . @math can effectively approximate various other top- @math definitions on uncertain data based on the value of parameter @math . An @math -relation consists of a number of @math -tuples, where @math -tuple is a set of mutually exclusive tuples (up to a constant number) called alternatives. Each @math -tuple in a relation randomly instantiates into one tuple from its alternatives. For an uncertain relation with @math tuples, our structure can answer top- @math queries in @math time, handles an update in @math time and takes @math space. Finally, we evaluate practical efficiency of our structure on both synthetic and real data.
Uncertain data management has attracted a lot of attention in recent years due to an increase in the number of application domains that naturally generate uncertain data. These include sensor networks @cite_19 , data cleaning @cite_4 and data integration @cite_2 @cite_14 . Several probabilistic data models have been proposed to capture data uncertainty (e.g TRIO @cite_16 , MYSTIQ @cite_11 , MayBMS @cite_17 , ORION @cite_6 , PrDB @cite_8 ). Virtually all models have adopted possible worlds semantics. Each data model captures tuple uncertainty (existence probabilities are attached to the tuples of the database), or attribute uncertainty (probability distributions are attached to the attributes) or both. Further distinction can be made among these models based on support for correlations. Most of the work in probabilistic databases has either assumed independence or supports restricted correlations, mutual exclusion being the most common. Recently proposed approaches @cite_8 @cite_3 extend the support for any arbitrary correlations.
@cite_14 @cite_4 @cite_8 @cite_17 @cite_6 @cite_3 @cite_19 @cite_2 @cite_16 @cite_11
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Several real-world applications need to effectively manage and reason about large amounts of data that are inherently uncertain. For instance, pervasive computing applications must constantly reason about volumes of noisy sensory readings for a variety of reasons, including motion prediction and human behavior modeling. Such probabilistic data analyses require sophisticated machine-learning tools that can effectively model the complex spatio temporal correlation patterns present in uncertain sensory data. Unfortunately, to date, most existing approaches to probabilistic database systems have relied on somewhat simplistic models of uncertainty that can be easily mapped onto existing relational architectures: Probabilistic information is typically associated with individual data tuples, with only limited or no support for effectively capturing and reasoning about complex data correlations. In this paper, we introduce BayesStore, a novel probabilistic data management architecture built on the principle of handling statistical models and probabilistic inference tools as first-class citizens of the database system. Adopting a machine-learning view, BAYESSTORE employs concise statistical relational models to effectively encode the correlation patterns between uncertain data, and promotes probabilistic inference and statistical model manipulation as part of the standard DBMS operator repertoire to support efficient and sound query processing. We present BAYESSTORE's uncertainty model based on a novel, first-order statistical model, and we redefine traditional query processing operators, to manipulate the data and the probabilistic models of the database in an efficient manner. Finally, we validate our approach, by demonstrating the value of exploiting data correlations during query processing, and by evaluating a number of optimizations which significantly accelerate query processing. Due to numerous applications producing noisy data, e.g., sensor data, experimental data, data from uncurated sources, information extraction, etc., there has been a surge of interest in the development of probabilistic databases. Most probabilistic database models proposed to date, however, fail to meet the challenges of real-world applications on two counts: (1) they often restrict the kinds of uncertainty that the user can represent; and (2) the query processing algorithms often cannot scale up to the needs of the application. In this work, we define a probabilistic database model, PrDB, that uses graphical models, a state-of-the-art probabilistic modeling technique developed within the statistics and machine learning community, to model uncertain data. We show how this results in a rich, complex yet compact probabilistic database model, which can capture the commonly occurring uncertainty models (tuple uncertainty, attribute uncertainty), more complex models (correlated tuples and attributes) and allows compact representation (shared and schema-level correlations). In addition, we show how query evaluation in PrDB translates into inference in an appropriately augmented graphical model. This allows us to easily use any of a myriad of exact and approximate inference algorithms developed within the graphical modeling community. While probabilistic inference provides a generic approach to solving queries, we show how the use of shared correlations, together with a novel inference algorithm that we developed based on bisimulation, can speed query processing significantly. We present a comprehensive experimental evaluation of the proposed techniques and show that even with a few shared correlations, significant speedups are possible. The invention comprises a method and apparatus for learning probabilistic models (PRM's) with attribute uncertainty. A PRM with attribute uncertainty defines a probability distribution over instantiations of a database. A learned PRM is useful for discovering interesting patterns and dependencies in the data. Unlike many existing techniques, the process is data-driven rather than hypothesis driven. This makes the technique particularly well-suited for exploratory data analysis. In addition, the invention comprises a method and apparatus for handling link uncertainty in PRM's. Link uncertainty is uncertainty over which entities are related in our domain. The invention comprises of two mechanisms for modeling link uncertainty: reference uncertainty and existence uncertainty. The invention includes learning algorithms for each form of link uncertainty. The third component of the invention is a technique for performing database selectivity estimation using probabilistic relational models. The invention provides a unified framework for the estimation of query result size for a broad class of queries involving both select and join operations. A single learned model can be used to efficiently estimate query result sizes for a wide collection of potential queries across multiple tables. Data uncertainty is inherent in many applications, including sensor networks, scientific data management, data integration, locationbased applications, etc. One of common queries for uncertain data is the probabilistic nearest neighbor (PNN) query that returns all uncertain objects with non-zero probabilities to be NN. In this paper we study the PNN query with a probability threshold (PNNT), which returns all objects with the NN probability greater than the threshold. Our PNNT query removes the assumption in all previous papers that the probability of an uncertain object always adds up to 1, i.e., we consider missing probabilities. We propose an augmented R-tree index with additional probabilistic information to facilitate pruning as well as global data structures for maintaining the current pruning status. We present our algorithm for efficiently answering PNNT queries and perform experiments to show that our algorithm significantly reduces the number of objects that need to be further evaluated as NN candidates.