### Abstract

The probabilistic-stream model was introduced by Jayram et al. [20]. It is a generalization of the data stream model that is suited to handling "probabilistic" data, where each item of the stream represents a probability distribution over a set of possible events. Therefore, a probabilistic stream determines a distribution over a potentially exponential number of classical "deterministic" streams where each item is deterministically one of the domain values. Designing efficient aggregation algorithms for probabilistic data is crucial for handling uncertainty in data-centric applications such as OLAP. Such algorithms are also useful in a variety of other setting including analyzing search engine traffic and aggregation in sensor networks. We present algorithms for computing commonly used aggregates on a probabilistic stream. We present the first one pass streaming algorithms for estimating the expected mean of a probabilistic stream, improving upon results in [20]. Next, we consider the problem of estimating frequency moments for probabilistic data. We propose a general approach to obtain unbiased estimators working over probabilistic data by utilizing unbiased estimators designed for standard streams. Applying this approach, we extend a classical data stream algorithm to obtain a one-pass algorithm for estimating F2, the second frequency moment. We present the first known streaming algorithms for estimating F0, the number of distinct items on probabilistic streams. Our work also gives an efficient one-pass algorithm for estimating the median of a probabilistic stream.

Original language | English (US) |
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Title of host publication | Proceedings of the Twenty-sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2007 |

Pages | 243-252 |

Number of pages | 10 |

DOIs | |

State | Published - Oct 29 2007 |

Event | 26th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2007 - Beijing, China Duration: Jun 11 2007 → Jun 13 2007 |

### Publication series

Name | Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems |
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### Conference

Conference | 26th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2007 |
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Country | China |

City | Beijing |

Period | 6/11/07 → 6/13/07 |

### Fingerprint

### Keywords

- Frequency moments
- Mean
- Median
- OLAP
- Probabilistic streams

### ASJC Scopus subject areas

- Software
- Information Systems
- Hardware and Architecture

### Cite this

*Proceedings of the Twenty-sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2007*(pp. 243-252). (Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems). https://doi.org/10.1145/1265530.1265565

**Estimating statistical aggregates on probabilistic data streams.** / Jayram, T. S.; McGregor, Andrew; Muthukrishnan, Shanmugavelayutham; Vee, Erik.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Twenty-sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2007.*Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 243-252, 26th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2007, Beijing, China, 6/11/07. https://doi.org/10.1145/1265530.1265565

}

TY - GEN

T1 - Estimating statistical aggregates on probabilistic data streams

AU - Jayram, T. S.

AU - McGregor, Andrew

AU - Muthukrishnan, Shanmugavelayutham

AU - Vee, Erik

PY - 2007/10/29

Y1 - 2007/10/29

N2 - The probabilistic-stream model was introduced by Jayram et al. [20]. It is a generalization of the data stream model that is suited to handling "probabilistic" data, where each item of the stream represents a probability distribution over a set of possible events. Therefore, a probabilistic stream determines a distribution over a potentially exponential number of classical "deterministic" streams where each item is deterministically one of the domain values. Designing efficient aggregation algorithms for probabilistic data is crucial for handling uncertainty in data-centric applications such as OLAP. Such algorithms are also useful in a variety of other setting including analyzing search engine traffic and aggregation in sensor networks. We present algorithms for computing commonly used aggregates on a probabilistic stream. We present the first one pass streaming algorithms for estimating the expected mean of a probabilistic stream, improving upon results in [20]. Next, we consider the problem of estimating frequency moments for probabilistic data. We propose a general approach to obtain unbiased estimators working over probabilistic data by utilizing unbiased estimators designed for standard streams. Applying this approach, we extend a classical data stream algorithm to obtain a one-pass algorithm for estimating F2, the second frequency moment. We present the first known streaming algorithms for estimating F0, the number of distinct items on probabilistic streams. Our work also gives an efficient one-pass algorithm for estimating the median of a probabilistic stream.

AB - The probabilistic-stream model was introduced by Jayram et al. [20]. It is a generalization of the data stream model that is suited to handling "probabilistic" data, where each item of the stream represents a probability distribution over a set of possible events. Therefore, a probabilistic stream determines a distribution over a potentially exponential number of classical "deterministic" streams where each item is deterministically one of the domain values. Designing efficient aggregation algorithms for probabilistic data is crucial for handling uncertainty in data-centric applications such as OLAP. Such algorithms are also useful in a variety of other setting including analyzing search engine traffic and aggregation in sensor networks. We present algorithms for computing commonly used aggregates on a probabilistic stream. We present the first one pass streaming algorithms for estimating the expected mean of a probabilistic stream, improving upon results in [20]. Next, we consider the problem of estimating frequency moments for probabilistic data. We propose a general approach to obtain unbiased estimators working over probabilistic data by utilizing unbiased estimators designed for standard streams. Applying this approach, we extend a classical data stream algorithm to obtain a one-pass algorithm for estimating F2, the second frequency moment. We present the first known streaming algorithms for estimating F0, the number of distinct items on probabilistic streams. Our work also gives an efficient one-pass algorithm for estimating the median of a probabilistic stream.

KW - Frequency moments

KW - Mean

KW - Median

KW - OLAP

KW - Probabilistic streams

UR - http://www.scopus.com/inward/record.url?scp=35448934923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448934923&partnerID=8YFLogxK

U2 - 10.1145/1265530.1265565

DO - 10.1145/1265530.1265565

M3 - Conference contribution

SN - 1595936858

SN - 9781595936851

T3 - Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

SP - 243

EP - 252

BT - Proceedings of the Twenty-sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2007

ER -