Results 1  10
of
469
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 542 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
SybilLimit: A nearoptimal social network defense against sybil attacks
 2008 [Online]. Available: http://www.comp.nus.edu.sg/~yuhf/sybillimittr.pdf
"... Abstract—Openaccess distributed systems such as peertopeer systems are particularly vulnerable to sybil attacks, where a malicious user creates multiple fake identities (called sybil nodes). Without a trusted central authority that can tie identities to real human beings, defending against sybil ..."
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Cited by 213 (7 self)
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Abstract—Openaccess distributed systems such as peertopeer systems are particularly vulnerable to sybil attacks, where a malicious user creates multiple fake identities (called sybil nodes). Without a trusted central authority that can tie identities to real human beings, defending against sybil attacks is quite challenging. Among the small number of decentralized approaches, our recent SybilGuard protocol leverages a key insight on social networks to bound the number of sybil nodes accepted. Despite its promising direction, SybilGuard can allow a large number of sybil nodes to be accepted. Furthermore, SybilGuard assumes that social networks are fastmixing, which has never been confirmed in the real world. This paper presents the novel SybilLimit protocol that leverages the same insight as SybilGuard, but offers dramatically improved and nearoptimal guarantees. The number of sybil nodes accepted is reduced by a factor of 2 ( p n), or around 200 times in our experiments for a millionnode system. We further prove that SybilLimit’s guarantee is at most a log n factor away from optimal when considering approaches based on fastmixing social networks. Finally, based on three largescale realworld social networks, we provide the first evidence that realworld social networks are indeed fastmixing. This validates the fundamental assumption behind SybilLimit’s and SybilGuard’s approach. Index Terms—Social networks, sybil attack, sybil identities, SybilGuard, SybilLimit. I.
A Stochastic Model of TCP/IP with Stationary Random Losses
 ACM SIGCOMM
, 2000
"... In this paper, we present a model for TCP/IP congestion control mechanism. The rate at which data is transmitted increases linearly in time until a packet loss is detected. At this point, the transmission rate is divided by a constant factor. Losses are generated by some exogenous random process whi ..."
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Cited by 209 (42 self)
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In this paper, we present a model for TCP/IP congestion control mechanism. The rate at which data is transmitted increases linearly in time until a packet loss is detected. At this point, the transmission rate is divided by a constant factor. Losses are generated by some exogenous random process which is assumed to be stationary ergodic. This allows us to account for any correlation and any distribution of interloss times. We obtain an explicit expression for the throughput of a TCP connection and bounds on the throughput when there is a limit on the window size. In addition, we study the effect of the Timeout mechanism on the throughput. A set of experiments is conducted over the real Internet and a comparison is provided with other models that make simple assumptions on the interloss time process. The comparison shows that our model approximates well the throughput of TCP for many distributions of interloss times.
General state space Markov chains and MCMC algorithm
 PROBABILITY SURVEYS
, 2004
"... This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform e ..."
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Cited by 177 (35 self)
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This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for MetropolisHastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.
On choosing and bounding probability metrics
 INTERNAT. STATIST. REV.
, 2002
"... When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a mea ..."
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Cited by 153 (2 self)
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When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.
Metropolized Independent Sampling with Comparisons to Rejection Sampling and Importance Sampling
, 1996
"... this paper, a special MetropolisHastings type algorithm, Metropolized independent sampling, proposed firstly in Hastings (1970), is studied in full detail. The eigenvalues and eigenvectors of the corresponding Markov chain, as well as a sharp bound for the total variation distance between the nth ..."
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Cited by 149 (4 self)
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this paper, a special MetropolisHastings type algorithm, Metropolized independent sampling, proposed firstly in Hastings (1970), is studied in full detail. The eigenvalues and eigenvectors of the corresponding Markov chain, as well as a sharp bound for the total variation distance between the nth updated distribution and the target distribution, are provided. Furthermore, the relationship between this scheme, rejection sampling, and importance sampling are studied with emphasizes on their relative efficiencies. It is shown that Metropolized independent sampling is superior to rejection sampling in two aspects: asymptotic efficiency and ease of computation. Key Words: Coupling, Delta method, Eigen analysis, Importance ratio. 1 1 Introduction
Finite Markov Chains and Algorithmic Applications
 IN LONDON MATHEMATICAL SOCIETY STUDENT TEXTS
, 2001
"... ..."
The Power of Two Random Choices: A Survey of Techniques and Results
 in Handbook of Randomized Computing
, 2000
"... ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately ..."
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Cited by 136 (6 self)
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ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log log n with high probability. Now suppose instead that the balls are placed sequentially, and each ball is placed in the least loaded of d 2 bins chosen independently and uniformly at random. Azar, Broder, Karlin, and Upfal showed that in this case, the maximum load is log log n= log d + (1) with high probability [ABKU99]. The important implication of this result is that even a small amount of choice can lead to drastically different results in load balancing. Indeed, having just two random choices (i.e.,...
Brownian motion and harmonic analysis on Sierpinski carpets
 MR MR1701339 (2000i:60083
, 1999
"... Abstract. We consider a class of fractal subsets of R d formed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to con ..."
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Cited by 106 (14 self)
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Abstract. We consider a class of fractal subsets of R d formed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusion X and determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting. 1