Abstract
We consider basic principles of probabilistic queries. Decomposition of a generic probabilistic query with conditioning in SQL-like syntax shows that data comparison operators are the only difference to the deterministic case. Any relational algebra operators presume comparison of attribute values. Probabilistic relational algebra operators are not comparable to deterministic ones due to uncertainty factor – they process distribution functions instead of unit values. We argue that chance constraint is a useful principle to build the basic set of binary probabilistic comparison operators (BPCO), the respective probabilistic relational algebra operators and their query syntax for query language implementations.
We argue that these BPCO should be based on principles of probability theory. We suggest generic expressions for the BPCO as counterparts for deterministic ones. Comparison of two random variables and a random variable to a scalar are considered. We give examples of BPCO application to uniformly distributed random variables and show how to build more complex probabilistic aggregation operators.
One of the main concerns is compatibility of uncertain query processing with query processing in modern deterministic relational databases. The advantage is knowledge continuity for developers and users of uncertain relational databases. With our approach, only addition of a probabilistic threshold to parameters of relational query operations is required for implementation. We demonstrate that the BPCO based on chance constraints maintain consistency of probabilistic query operators with the syntax of deterministic query operators that are common in today’s database industrial query languages like SQL.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barbará, D., Garcia-Molina, H., Porter, D.: The management of probabilistic data. IEEE Trans. Knowl. Data Eng. 4(5), 487–502 (1992). https://doi.org/10.1109/69.166990
Tran, T.L.T., McGregor, A., Diao, Y., Peng, L., Liu, A.: Conditioning and aggregating uncertain data streams: going beyond expectations. PVLDB 3(1), 1302–1313 (2010). https://doi.org/10.14778/1920841.1921001
Wang, Y., Li, X., Li, X., Wang, Y.: A survey of queries over uncertain data. Knowl. Inf. Syst. 37(3), 485–530 (2013). https://doi.org/10.1007/s10115-013-0638-6
Van den Broeck, G., Suciu, D.: Query processing on probabilistic data: a survey. Found. Trends Databases 7(3–4), 197–341 (2017). https://doi.org/10.1561/1900000052
Tran, T.L.T., Peng, L., Diao, Y., McGregor, A., Liu, A.: CLARO: modeling and processing uncertain data streams. VLDB J. 21(5), 651–676 (2012). https://doi.org/10.1007/s00778-011-0261-7
Ge, T., Zdonik, S.: Handling uncertain data in array database systems. In: Alonso, G., Blakeley, J. A., Chen, A.L.P. (eds.) ICDE 2008, pp. 1140–1149. IEEE Computer Society (2008). https://doi.org/10.1109/ICDE.2008.4497523
Dezfuli, M.G., Haghjoo, M.S.: Xtream: a system for continuous querying over uncertain data streams. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds.) SUM 2012. LNCS (LNAI), vol. 7520, pp. 1–15. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33362-0_1
Garcia-Molina, H., Ullman, J.D., Widom, J.: Database Systems - The Complete Book. 2nd edn. Pearson Education (2009)
Henrion, R.: Chance constrained problems. https://www.stoprog.org/sites/default/files/tutorials/SP10/Henrion.pdf. Accessed 21 May 2021
Fuhr, N.: A probabilistic framework for vague queries and imprecise information in databases. In: McLeod, D., Sacks-Davis, R., Schek, H.J. (eds.) VLDB 1990, pp. 696–707. Morgan Kaufmann (1990). http://www.vldb.org/conf/1990/P696.PDF
Geletu, A., Klöppel, M., Zhang, H., Li, P.: Advances and applications of chance-constrained approaches to systems optimisation under uncertainty. Int. J. Syst. Sci. 44(7), 1209–1232 (2013). https://doi.org/10.1080/00207721.2012.670310
Prékopa, A.: Stochastic Programming. Springer, Dordrecht (2011). https://doi.org/10.1007/978-94-017-3087-7
Sadooghi-Alvandi, S.M., Nematollahi, A.R., Habib, R.: On the distribution of the sum of independent uniform random variables. Stat. Papers 50(1), 171–175 (2007). https://doi.org/10.1007/s00362-007-0049-4
Cheng, R., Kalashnikov, D.V., Prabhakar, S.: Querying imprecise data in moving object environments. IEEE Trans. Knowl. Data Eng. 16(9), 1112–1127 (2004). https://doi.org/10.1109/TKDE.2004.46
Fuhr, N., Thomas Rölleke, T.: A probabilistic relational algebra for the integration of information retrieval and database systems. ACM Trans. Inf. Syst. 15(1), 32–66 (1997). https://doi.org/10.1145/239041.239045
Goman, M.: Efficient aggregation methods for probabilistic data streams. In: Shishkov, B. (ed.) BMSD 2018. LNBIP, vol. 319, pp. 116–132. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94214-8_8
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Goman, M. (2021). Chance Constraint as a Basis for Probabilistic Query Model. In: Bellatreche, L., Dumas, M., Karras, P., Matulevičius, R. (eds) Advances in Databases and Information Systems. ADBIS 2021. Lecture Notes in Computer Science(), vol 12843. Springer, Cham. https://doi.org/10.1007/978-3-030-82472-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-82472-3_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-82471-6
Online ISBN: 978-3-030-82472-3
eBook Packages: Computer ScienceComputer Science (R0)