Confidence intervals for the number of unseen types

Finkelstein, Mark; Tucker, Howard G.; Veeh, Jerry Alan

doi:10.1016/s0167-7152(97)00146-6

Cited by 28 publications

(20 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Intuitively, the size estimateñ is chosen such that the observed number of non-unique elements is equal to its expectation. As a remark, if the node distribution is uniform, this estimator is identical to the maximum likelihood estimator [7].…”

Section: Non-unique Element Counting Es-timatormentioning

confidence: 98%

“…Surprisingly, taking only O( √ n) samples can guarantee that this estimate for n is rather accurate. 5 In [7] the authors present a maximum likelihood estimator for this problem and show that their estimator converges almost surly when the number of samples increases. In [6,10] the authors extend these methods to non-uniform, but known, distributions.…”

Section: Background and Prior Workmentioning

confidence: 99%

See 1 more Smart Citation

Estimating Sizes of Social Networks via Biased Sampling

Katzir¹,

Liberty

Somekh³

et al. 2014

Internet Mathematics

View full text Add to dashboard Cite

Online social networks have become very popular in recent years and their number of users is already measured in many hundreds of millions. For various commercial and sociological purposes, an independent estimate of their sizes is important. In this work, algorithms for estimating the number of users in such networks are considered. The proposed schemes are also applicable for estimating the sizes of networks' sub-populations. The suggested algorithms interact with the social networks via their public APIs only, and rely on no other external information. Due to obvious traffic and privacy concerns, the number of such interactions is severely limited. We therefore focus on minimizing the number of API interactions needed for producing good size estimates. We adopt the abstraction of social networks as undirected graphs and use random node sampling. By counting the number of collisions or non-unique nodes in the sample, we produce a size estimate. Then, we show analytically that the estimate error vanishes with high probability for smaller number of samples than those required by prior-art algorithms. Moreover, although our algorithms are provably correct for any graph, they excel when applied to social network-like graphs. The proposed algorithms were evaluated on synthetic as well real social networks such as Facebook, IMDB, and DBLP. Our experiments corroborated the theoretical results, and demonstrated the effectiveness of the algorithms.

show abstract

Section: Non-unique Element Counting Es-timatormentioning

confidence: 98%

Section: Background and Prior Workmentioning

confidence: 99%

Estimating Sizes of Social Networks via Biased Sampling

Katzir¹,

Liberty

Somekh³

et al. 2014

Internet Mathematics

View full text Add to dashboard Cite

show abstract

“…Occupancy models play an important role in the analysis of capture/recapture techniques for population estimation, as for example in ecology, pathology, and software fault detection [1], [3], [9], [14], [15]. In this approach, individuals in the population are 'captured' at random and the population size is inferred from the rate at which individuals are 'recaptured'.…”

Section: Introductionmentioning

confidence: 99%

Large Deviations Principle for Occupancy Problems with Colored Balls

2007

View full text Add to dashboard Cite

A large deviations principle (LDP), demonstrated for occupancy problems with indistinguishable balls, is generalized to the case in which balls are distinguished by a finite number of colors. The colors of the balls are chosen independently from the occupancy process itself. There are r balls thrown into n urns with the probability of a ball entering a given urn being 1/n (i.e. Maxwell-Boltzmann statistics). The LDP applies with the scale parameter, n, tending to infinity and r increasing proportionally. The LDP holds under mild restrictions, the key one being that the coloring process by itself satisfies an LDP. This includes the important special cases of deterministic coloring patterns and colors chosen with fixed probabilities independently for each ball.

show abstract

“…Once the recipients collect one value of all the one-way chains, they can reconstruct the public key of the specific time slot and validate the signature, and hence validate all subsequent signatures. The "coupon collector" problem predicts that after collection t ln(t) random V's on average the recipients will have one value of every chain [19].…”

Section: Authentication With One-way Chainsmentioning

confidence: 99%

Power consumption evaluation of efficient digital signature schemes for low power devices

Seys

Preneel

WiMob'2005), IEEE International Conference on Wireless and Mobile Computing, Networking and Communications, 2005.

View full text Add to dashboard Cite

Abstract-In this paper we evaluate the power consumption of different digital signature schemes. We compare the cost of the Elliptic Curve Digital Signature Algorithm with signature schemes solely based on symmetric techniques such as the DiffieLamport one-time signature scheme. These evaluations take into account all aspects of using digital signatures in wireless environments: energy consumption of key generation, signing and verification, and the communication cost of sending and receiving the necessary data (including the public keys and the necessary data to authenticate them).

show abstract

Confidence intervals for the number of unseen types

Cited by 28 publications

References 2 publications

Estimating Sizes of Social Networks via Biased Sampling

Estimating Sizes of Social Networks via Biased Sampling

Large Deviations Principle for Occupancy Problems with Colored Balls

Power consumption evaluation of efficient digital signature schemes for low power devices

Contact Info

Product

Resources

About