New bounds on the probability of a finite union of events

Yang, Jun; Alajaji, Fady; Takahara, Glen

doi:10.1109/isit.2014.6875037

Cited by 5 publications

(10 citation statements)

References 19 publications

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“…We derive two new classes of lower bounds of at most pseudo-polynomial computational complexity. These classes of lower bounds generalize the existing bound in [18] and recent bounds in [32,33] and are numerically shown to be tighter in some cases than the Gallot-Kounias bound [14,17] and the Prékopa-Gao bound [26] which require more information on the events probabilities.…”

supporting

confidence: 61%

“…, N }. Recently, using the same partial information as the KAT bound, i.e., {P (A i )} and { j:j =i P (A i ∩ A j )}, the optimal lower/upper bound as well as a new analytical bound which is sharper than the KAT bound were developed by Yang-Alajaji-Takahara in [32,33] (for convenience, these two bounds are respectively referred to as the YAT-I and YAT-II bounds).…”

mentioning

confidence: 99%

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On bounding the union probability using partial weighted information

Yang

Alajaji

Takahara

2016

Statistics & Probability Letters

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This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs for some of the existing bounds are provided and new observations regarding the existing Gallot-Kounias bound are given. References 16Recent works: We close this survey by referring the reader to [YAT14; YAT15a; YAT15b; YAT16a; YAT16b] for the most recent works on this topic.

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supporting

confidence: 61%

mentioning

confidence: 99%

On bounding the union probability using partial weighted information

Yang

Alajaji

Takahara

2016

Statistics & Probability Letters

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“…Thus, future evaluations of our algorithm will definitely benefit from analysis of achievable secrecy rate region with polar alignment for the general Gaussian MACW channel. Finally, application of new upper/lower bounds in [19] will be essential in improving the block error rate analysis/ simulations in future.…”

Section: Discussionmentioning

confidence: 99%

Cooperative jamming polar codes for multiple‐access wiretap channels

Hajimomeni¹,

Aghaeinia²,

Kim³

et al. 2016

IET Communications

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“…In , the authors propose a lower bound of order two, called as YAT, which is shown to be stronger than the classical Bonferroni bound of order two. For a given subset S of V of size k , YAT is computed as

β + \sum_{i \in S} {normalα}_{i} true(\frac{1}{χ true(\frac{{normalγ}_{i}}{{normalα}_{i}} true)} - \frac{\frac{{normalγ}_{i}}{{normalα}_{i}} - χ true(\frac{{normalγ}_{i}}{{normalα}_{i}} true)}{true[1 + χ true(\frac{{normalγ}_{i}}{{normalα}_{i}} true) true] true[χ true(\frac{{normalγ}_{i}}{{normalα}_{i}} true) true]} true) \leq \overset{true¯}{G B N} (S),

where

χ (.)

is a function defined as

χ (x) = true{\begin{matrix} x - 1 & if x \geq 2 is an integer, \\ true⌊ x true⌋ & otherwise, \end{matrix}

β = \max true{0, \max_{i \in S} true{\sum_{j \in S} P (i, j) - (k - 1) P (i) true} true}, {normalα}_{i} = P ...

…”

Section: Computation Of the New Boundsmentioning

confidence: 99%

“…In three network and group size combination, YAT beats KAT in terms of the percentage of finding the best bound. In our further computational experiments, we will use YAT since it is both experimentally and theoretically better than KAT . When the group size is 3, upper bounds KCBu and HW find the same bounds for all the groups.…”

Section: Computational Experimentsmentioning

confidence: 99%

Faster computation of successive bounds on the group betweenness centrality

Dinler

Tural

2018

Networks

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We propose a method that computes bounds on the group betweenness centrality (GBC) of groups of vertices of a network. Once certain quantities related to the network are computed in the preprocessing step that takes O ( n 3 ) time, where n is the number of vertices in the network, our method can compute bounds on the GBC of any number of groups of vertices successively, for each group requiring a running time proportional to the square of its size. Our method is an improvement of the method of Kolaczyk et al. [Social Networks, 31, 3 (2009)], which has to be restarted for each group making it less efficient for the successive GBC computations. In addition, the bounds used in our method are stronger and/or faster to compute. Our computational experiments show that in the search for a group of a certain size with the highest GBC value, our method reduces the number of candidate groups substantially and in some cases the optimal group can be found without exactly computing the GBC values which is computationally more demanding.

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New bounds on the probability of a finite union of events

Cited by 5 publications

References 19 publications

On bounding the union probability using partial weighted information

On bounding the union probability using partial weighted information

Cooperative jamming polar codes for multiple‐access wiretap channels

Faster computation of successive bounds on the group betweenness centrality

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