A Histogram Method for Summarizing Multi-dimensional Probabilistic Data

Iqbal, Ashraf Mohammed; Wang, Hai H.; Gao, Qigang

doi:10.1016/j.procs.2013.06.135

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…This is also true in uncertain counterpart. Therefore, [9], [15], [16] proposed to construct optimal histograms and wavelets over uncertain datasets to approximate the probabilistic distribution of these datasets. They also illustrated how to optimize a query by using the approximated distributions.…”

Section: B Summarization Of Uncertain Datamentioning

confidence: 99%

“…Most of them involved estimating single statistical aggregate [11]- [14], e.g., minimum and maximum values, sum, average, and count; such summaries, however, could support only simple applications [4]. To obtain summaries of probabilistic data and support more complex applications, some of them proposed algorithms to compute optimal histogram or wavelet [9], [15], [16] on the data under possible worlds semantics, but the proposed algorithms could only handle static datasets with existential uncertainty drawn from a discrete domain of limited size, and thus were not capable of extending their use to uncertain data streams or datasets with value uncertainty drawn from a continuous domain space. Reference [5] summarized uncertain data streams by computing essential aggregates, but their methods did not apply to continuous domain either.…”

Section: Introductionmentioning

confidence: 99%

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Online Computing Quantile Summaries Over Uncertain Data Streams

Liang

Liu

2019

IEEE Access

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Quantile summarization is a useful tool in data streams management and mining that can efficiently capture the distribution of the data. A quantile of a sequence of points is the point with a given rank in the sequence. Given a sequence of uncertain points S on the real line, each represented by one-dimensional probability density function (pdf), we study the problem of incrementally maintaining quantile summaries on S such that for any query with a given rank, the summaries can provide a point as the quantile within a given error. We define quantile on uncertain data with discrete or continuous pdf in terms of two error metrics under possible worlds semantics. For an answer to a quantile query on uncertain data, we give the methods for calculating the value of the error and thereby discussing the high-level features of the summaries that can answer approximate quantile query under the two error metrics. We propose an online, space efficient algorithm to compute such summary data on uncertain data streams. The experimental results show that our algorithm substantially outperforms other techniques, such as Monte Carlo and averaging methods, in terms of query error and space for storing the summary data. INDEX TERMS Data preprocessing, possible worlds, quantile summaries, uncertain data streams.

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Section: B Summarization Of Uncertain Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Online Computing Quantile Summaries Over Uncertain Data Streams

Liang

Liu

2019

IEEE Access

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“…In order to provide approximate answers, these systems are based on consolidated methodologies such as summary tables (Gupta & Quaas, 1995;Huang et al, 2014), sampling (Acharya et al, 1999a;Acharya et al, 1999b;Rösch & Lehner, 2009;Gibbons et al, 1998), histograms (Poosala et al, 1999;Chen & Dobra, 2013;Cormode et al, 2009;Iqbal et al, 2013), wavelets (Chakrabarti et al 2001;Guha et al, 2008), orthonormal series (Lefons et al, 1995;Yan et al, 2007), probabilistic models (Mannila & Smyth, 2000;Missaoui et al, 2007), and clustering (Shanmugasundaram et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

Benchmark for Approximate Query Answering Systems

Tria

Lefons

Tangorra

2015

Journal of Database Management

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The standard benchmark for Decision Support Systems is TPC-H, which is composed of a database, a workload, and a set of metrics for the performance evaluation. However, TPC-H does not include a methodology for the benchmark of Approximate Query Answering Systems, or the software tools used to obtain fast answers to analytical queries in the decision making process. In the paper, the authors present a methodology to evaluate and compare Approximate Query Answering Systems. To this aim, a methodology that extends the standard TPC-H and a set of new metrics that take into account the specific features of these systems are proposed. Experimental results show the application of these metrics to two systems based on the data analytic approximation by orthonormal series.

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