Probabilistic Relational Databases Research Articles

A relational database model and algebra integrating fuzzy attributes and probabilistic tuples

Although there have been many fuzzy or probabilistic relational database models proposed for representing and handling imprecise and uncertain information of objects in real-world applications, models combining the relevance and strength of both fuzzy set theory and probability theory appear sporadic. In this paper, we propose a new fuzzy and probabilistic relational database model where the imprecision of an attribute value is represented by a fuzzy set and the uncertainty of a relational tuple is represented by a probability interval. The mass assignment theory is employed to deal with the challenge of integration and computation of both fuzzy sets and probabilities in the same model. The conjunction and disjunction strategies to combine imprecise and uncertain information are introduced. Then the fundamental concepts of the classical relational database model are extended and generalized in this new model. The syntax and semantics of the selection operation are formally defined. Finally, the other important algebraic operations on imprecise attributes and uncertain tuples are developed.

A Relational-Database Methodology for Incorporating Consciousness into AI Agents

Consciousness is key to Artificial General Intelligence. It is currently unclear what is consciousness and we expect that by the time it is understood, there will probably be millions of man-years invested in the development of AI agents. This paper addresses the following question. How should AI agents be engineered from now on, such that when it becomes clear how consciousness and subjective experiences are generated, the effort of endowing AI agents and robots existing at that time with consciousness is minimized. As far as we know this question has not been studied heretofore. The paper proposes a methodology and architecture that are based on evolving Probabilistic Relational Databases, and on stepwise progressive data fusion. The methodology and architecture are independent of what consciousness turns out to be, provided that it can be incorporated into AI agents.

Query with Assumptions for Probabilistic Relational Databases

Query with Assumptions for Probabilistic Relational Databases

EXTENDING RELATIONAL DATABASE MODEL FOR UNCERTAIN INFORMATION

In this paper, we propose a new probabilistic relational database model, denote by PRDB, as an extension of the classical relational database model where the uncertainty of relational attribute values and tuples are respectively represented by finite sets and probability intervals. A probabilistic interpretation of binary relations on finite sets is proposed for the computation of their probability measures. The combination strategies on probability intervals are employed to combine attribute values and compute uncertain membership degrees of tuples in a relation. The fundamental concepts of the classical relational database model are extended and generalized for PRDB. Then, the probabilistic relational algebraic operations are formally defined accordingly in PRDB. In addition, a set of the properties of the algebraic operations in this new model also are formulated and proven.

Reengineering Probabilistic Relational Databases with Fuzzy Probability Measures into XML Model

This paper concentrates on modeling probabilistic events with fuzzy probability measures in relational databases and XML (Extensible Markup Language). Instead of crisp probability degrees or interval probability degrees, fuzzy sets are applied to represent imprecise probability degrees in relational databases and XML. A probabilistic XML model with fuzzy probability measures is introduced, which incorporates fuzzy probability measures to handle imprecision and uncertainty. In particular, the formal approach to reengineering the relational database model with fuzzy probability measures into the DTD (document type definition) model with fuzzy probability measures is developed in the paper.

A probabilistic relational database model and algebra

This paper introduces a probabilistic relational database model, called PRDB, for representing and querying uncertain information of objects in practice. To develop the PRDB model, first, we represent the relational attribute value as a pair of probabilistic distributions on a set for modeling the possibility that the attribute can take one of the values of the set with a probability belonging to the interval which is inferred from the pair of probabilistic distributions. Next, on the basis representing such attribute values, we formally define the notions as the schema, relation, probabilistic functional dependency and probabilistic relational algebraic operations for PRDB. In addition, a set of the properties of the probabilistic relational algebraic operations in PRDB also are formulated and proven.

On efficient conditioning of probabilistic relational databases

A probabilistic relational database is a probability distribution over a set of deterministic relational databases (namely, possible worlds). Efficient updating information in probabilistic databases is required in several applications, such as sensor networking and data cleaning. As a way to update a probabilistic database, conditioning refines the probability distribution of the possible worlds based on general knowledge, such as functional dependencies. The existing methods for conditioning are exponential over the number of variables in the probabilistic database for an arbitrary constraint. In this paper, a constraint-based conditioning framework is proposed, which solves the conditioning problem by considering only the variables in the given constraint. Then, we prove the correctness of our proposed approach and provide efficient algorithms for each step of the approach. Afterward, a pruning strategy that can significantly improve the efficiency of the constraint-based approach is proposed for the functional dependency constraints. Furthermore, for functional dependency constraints, a variable-elimination strategy that minimizes the number of generated variables can benefit the subsequent query processing. The experimental study shows that the constraint-based approach is more efficient than other approaches described in the literature. The effectiveness of the two optimization strategies for functional dependency constraints is also demonstrated in the experiment.

Top-k best probability queries and semantics ranking properties on probabilistic databases

There has been much interest in answering top-k queries on probabilistic data in various applications such as market analysis, personalized services, and decision making. In probabilistic relational databases, the most common problem in answering top-k queries (ranking queries) is selecting the top-k result based on scores and top-k probabilities. In this paper, we firstly propose novel answers to top-k best probability queries by selecting the probabilistic tuples which have not only the best top-k scores but also the best top-k probabilities. An efficient algorithm for top-k best probability queries is introduced without requiring users to define a threshold. The top-k best probability approach is more efficient and effective than the probability threshold approach (PT-k) [1,2]. Second, we add the “k-best ranking score” into the set of semantic properties for ranking queries on uncertain data proposed by [3,4]. Then, our proposed method is analyzed, which meets the semantic ranking properties on uncertain data. In addition, it proves that the answers to the top-k best probability queries overcome drawbacks of previous definitions of the top-k queries on probabilistic data in terms of semantic ranking properties. Lastly, we conduct an extensive experimental study verifying the effectiveness of answers to the top-k best probability queries compared to PT-k queries on uncertain data and the efficiency of our algorithm against the state-of-the-art execution of the PT-k algorithm using both real and synthetic data sets.

Information-theoretic characterizations of conditional mutual independence and Markov random fields

We take the point of view that a Markov random field is a collection of so-called full conditional mutual independencies. Using the theory of I-measure, we have obtained a number of fundamental characterizations related to conditional mutual independence and Markov random fields. We show that many aspects of conditional mutual independence and Markov random fields have very simple set-theoretic descriptions. New insights into the structure of conditional mutual independence and Markov random fields are obtained. Our results have immediate applications in the implication problem of probabilistic conditional independency and relational database. We obtain a hypergraph characterization of a Markov random field which makes it legitimate to view a Markov random field as a hypergraph. Based on this result, we naturally employ the Graham reduction, a tool from relational database theory, to recognize a Markov forest. This connection between Markov random fields and hypergraph sheds some light on the possible role of hypergraph theory in the study of Markov random fields.

Modifications of Uncertain Data: A Bayesian Framework for Belief Revision

The inherent uncertainty pervasive over the real world often forces business decisions to be made using uncertain data. The conventional relational model does not have the ability to handle uncertain data. In recent years, several approaches have been proposed in the literature for representing uncertain data by extending the relational model, primarily using probability theory. The aspect of database modification, however, has not been addressed in prior research. It is clear that any modification of existing probabilistic data, based on new information, amounts to the revision of one's belief about real-world objects. In this paper, we examine the aspect of belief revision and develop a generalized algorithm that can be used for the modification of existing data in a probabilistic relational database. The belief revision scheme is shown to be closed, consistent, and complete.

Query evaluation in probabilistic relational databases

This paper describes a generalization of the relational model in order to capture and manipulate a type of probabilistic information. Probabilistic databases are formalized by means of logic theories based on a probabilistic first-order language proposed by Halpern. A sound and complete method is described for evaluating queries in probabilistic theories. The generalization proposed can be incorporated into existing relational systems with the addition of a component for manipulating propositional formulas.

An Extended Relational Data Model For Probabilistic Reasoning

Probabilistic methods provide a formalism for reasoning about partial beliefs under conditions of uncertainty. This paper suggests a new representation of probabilistic knowledge. This representation encompasses the traditional relational database model. In particular, it is shown that probabilistic conditional independence is equivalent to the notion of generalized multivalued dependency. More importantly, a Markov network can be viewed as a generalized acyclic join dependency. This linkage between these two apparently different but closely related knowledge representations provides a foundation for developing a unified model for probabilistic reasoning and relational database systems.