Inequalities for the probability of the occurrence of at least m out of n events

Sathe, Y. S.; Pradhan, Meena; Shah, S. P.

doi:10.1017/s002190020009745x

Cited by 21 publications

(14 citation statements)

References 2 publications

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“…The theorem improves the upper bound obtained by Sathe et al (1980), result 4. Their bound is identical to (15) with i given by the r.h.s.…”

Section: Derivation Of the Probability Boundsupporting

confidence: 80%

A sharp upper probability bound for the occurrence of at least m out of n events

Platz¹

1985

Journal of Applied Probability

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Consider a fixed set of n events. Let S1 denote the sum of the probabilities of occurrence of each event and S2 the sum of the probabilities of occurrence of each of the pairs of events. Using a dual linear programming method a sharp upper bound is derived for the probability of occurrence of at least m out of the n events when S1 and S2 are given. The bound improves one of the inequalities obtained by Sathe et al. (1980).

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“…The theorem improves the upper bound obtained by Sathe et al (1980), result 4. Their bound is identical to (15) with i given by the r.h.s.…”

Section: Derivation Of the Probability Boundsupporting

confidence: 80%

A sharp upper probability bound for the occurrence of at least m out of n events

Platz¹

1985

Journal of Applied Probability

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“…Theorems 3.2 and 3.3 in the case r = 2 leads to the results by Kwerel (1975a), Sathe et al (1980) and Platz (1985). The derivation is simple and is omitted.…”

Section: Most Stringent Inequalities Based On (M1 M2 1143)mentioning

confidence: 86%

Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]

Sibuya

1991

Ann Inst Stat Math

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“…According to the de Caen probability inequality [8] and the Kwerel probability inequality [16], we can obtain the following lower upper and the upper bound of P r(SI1 ∨ · · · ∨ SIm), respectively.…”

Section: Probabilistic Bounding-based Feature Selectionmentioning

confidence: 99%

Efficient Probabilistic Supergraph Search Over Large Uncertain Graphs

Tong

Zhang

Cao

et al. 2014

Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management

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In recent years, with the emergence of a number of new real applications, such as protein-protein interaction (PPI) networks, visual pattern recognition, and intelligent traffic systems, managing huge volumes of uncertain graphs has attracted much attention in the database community. Currently, most existing fundamental queries over graphs only support deterministic (or certain) graphs, although real graph data are often noisy, inaccurate, and incomplete. In this paper, we study a new type of uncertain graph query, probabilistic supergraph containment query over large uncertain graphs. Specifically, given an uncertain graph database UGD which contains a set of uncertain graphs, a deterministic query graph q, and a probabilistic threshold δ, a probabilistic supergraph containment query is to find the set of uncertain graphs from UGD, denoted as UGDq, such that UGDq = {ugi ∈ UGD|P r(ugi ⊆ q) ≥ δ} where P r(ugi ⊆ q) means the likelihood that ugi is a subgraph of q. We prove that the computation of P r(ugi ⊆ q) is #P-hard and design an efficient filtering-and-verification framework to avoid the expensive computation. In particular, we propose an effective filtering strategy and a novel probabilistic inverted index, called PS-Index, to enhance pruning power in the filtering phase. Furthermore, the candidate graphs which pass the filtering phase are tested in the verification phase via an efficient unequal probability sampling-based approximation algorithm. Finally, we verify the effectiveness and efficiency of the proposed methods through extensive experiments.

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Inequalities for the probability of the occurrence of at least m out of n events

Cited by 21 publications

References 2 publications

A sharp upper probability bound for the occurrence of at least m out of n events

A sharp upper probability bound for the occurrence of at least m out of n events

Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]

Efficient Probabilistic Supergraph Search Over Large Uncertain Graphs

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