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Hypergeometric tail inequalities: ending the insanity
TLDR
The hypergeometric distribution is briefly and informally surveyed in this paper, including popular notation, symmetries, and the tail inequalities $Pr[i \ge E[i]-tn] \le e^{-2t^2n}$ andAbstract:
The hypergeometric distribution is briefly and informally surveyed, including popular notation, symmetries, and the tail inequalities $Pr[i \ge E[i]+tn] \le e^{-2t^2n}$ and $Pr[i \le E[i]-tn] \le e^{-2t^2n}$.read more
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Proceedings ArticleDOI
Scalable Bias-Resistant Distributed Randomness
Ewa Syta,Philipp Jovanovic,Eleftherios Kokoris Kogias,Nicolas Gailly,Linus Gasser,Ismail Khoffi,Michael J. Fischer,Bryan Ford +7 more
TL;DR: This paper proposes two large-scale distributed protocols, RandHound and RandHerd, which provide publicly-verifiable, unpredictable, and unbiasable randomness against Byzantine adversaries.
Journal ArticleDOI
Network Cross-Validation for Determining the Number of Communities in Network Data
Kehui Chen,Jing Lei +1 more
TL;DR: In this paper, the authors developed an efficient network cross-validation (NCV) approach to determine the number of communities, as well as to choose between the regular stochastic block model and the degree corrected block model (DCBM).
Posted Content
Scalable Bias-Resistant Distributed Randomness.
Proceedings ArticleDOI
TRIÈST: Counting Local and Global Triangles in Fully-Dynamic Streams with Fixed Memory Size
TL;DR: This work presents TRIEST, a suite of one-pass streaming algorithms to compute unbiased, low-variance, high-quality approximations of the global and local number of triangles in a fully-dynamic graph represented as an adversarial stream of edge insertions and deletions.
Proceedings Article
Greed Is Good: Near-Optimal Submodular Maximization via Greedy Optimization
TL;DR: In this article, it was shown that invoking the classical greedy algorithm $O(sqrt{k})$-times leads to the (currently) fastest deterministic algorithm, called Repeated Greedy, for maximizing a general submodular function subject to $k$-independent system constraints.
References
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Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.