Abstract
Though extensions of the relational model of data have been proposed to handle probabilistic information, there has been no work to date on handling aggregate operators in such databases. In this paper, we show how classical aggregation operators (like COUNT, SUM, etc.) as well as other statistical operators (like weighted average, variance, etc.) can be defined as well as implemented over probabilistic databases. We define these operations, develop a formal linear program model for computing answers to such queries, and then develop a generic algorithm to compute aggregates.
Keywords
- Relational Algebra
- Probability Interval
- Aggregate Function
- Deductive Database
- Linear Programming Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D. Barbara, H. Garcia-Molina, and D. Porter. (1992) The Management of Probabilistic Data, IEEE Trans. on Knowledge and Data Engineering, Vol. 4, pps 487–502.
R. Cavallo and M. Pittarelli. (1987) The Theory of Probabilistic Databases, in Proc. VLDB’87.
T.H. Cormen, C.E. Leiserson, and R.L. Rivest. (1992) Introduction to Algorithms, MIT Press, Cambridge.
A. Dekhtyar, R. Ross, and V.S. Subrahmanian, Probabilistic Temporal Databases, Part I: Algebra, ACM Transactions on Database Systems, Vol. 26, 1.
D. Dey and S. Sarkar. (1996) A Probabilistic Relational Model and Algebra, A CM Transactions on Database Systems, Vol. 21, 3, pps 339–369.
C. Dyreson and R. Snodgrass. (1998) Supporting Valid-Time Indeterminacy, ACM Transactions on Database Systems, Vol. 23, Nr. 1, pps 1–57.
T. Eiter, T. Lukasiewicz, and M. Walter. Extension of the relational algebra to probabilistic complex values. In Proceedings of the International Symposium on Foundations of Information and Knowledge Systems (Fo IKS 2000), Volume 1762 of LNCS (2000), pp. 94–115. Springer.
R. Fagin, J. Halpern, and N. Megiddo. (1990) A logic for reasoning about probabilities. Information and Computation 87, 78–128.
N. Fuhr and T. Rolleke. (1996) A probabilistic NF2 relational algebra for integrated information retrieval and database systems. ACM Transactions on Information Systems, 15, 1, 32–66.
G. Kamberova and R. Bajcsy. (1998) Stereo Depth Estimation: the Confidence Interval Approach, Proc. Intl. Conf. Computer Vision ICCV98, Bombay, India, Jan. 1998
W. Kiessling, H. Thone, and U. Guntzer. (1992) Database Support for Problematic Knowledge, in Proc. EDBT-92, pp. 421–436, Springer LNCS Vol. 580.
V.S. Lakshmanan, N. Leone, R. Ross, and V.S. Subrahmanian. (1996) Prob View: A Flexible Probabilistic Database System. ACM Transactions on Database Systems, Vol. 22, Nr. 3, pp. 419–469.
V.S. Lakshmanan and F. Sadri. (1994) Modeling Uncertainty in Deductive Databases, in Proc. Int. Conf. on Database Expert Systems and Applications, (DEXA’94), Lecture Notes in Computer Science, Vol. 856, Springer (1994), pp. 724–733.
V.S. Lakshmanan and F. Sadri. (1994) Probabilistic Deductive Databases, in Proc. Int. Logic Programming Symp., (ILPS’94), MIT Press.
W. N. Street, O. L. Mangasarian, and W.H. Wolberg. (1995) An inductive learning approach to prognostic prediction. Proceedings of the Twelfth International Conference on Machine Learning, A. Prieditis and S. Russell, eds., pages 522–530, Morgan Kaufmann, 1995.
J.D. Ullman. (1989) Principles of Database and Knowledge Base Systems, Computer Science Press, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ross, R., Subrahmanian, V.S., Grant, J. (2002). Probabilistic Aggregates. In: Hacid, MS., Raś, Z.W., Zighed, D.A., Kodratoff, Y. (eds) Foundations of Intelligent Systems. ISMIS 2002. Lecture Notes in Computer Science(), vol 2366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48050-1_59
Download citation
DOI: https://doi.org/10.1007/3-540-48050-1_59
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43785-7
Online ISBN: 978-3-540-48050-1
eBook Packages: Springer Book Archive