The randomness recycler: a new technique for perfect sampling

@article{Fill2000TheRR,
  title={The randomness recycler: a new technique for perfect sampling},
  author={James Allen Fill and Mark L. Huber},
  journal={Proceedings 41st Annual Symposium on Foundations of Computer Science},
  year={2000},
  pages={503-511}
}
  • J. A. Fill, M. Huber
  • Published 29 September 2000
  • Mathematics
  • Proceedings 41st Annual Symposium on Foundations of Computer Science
For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional Markov chain methods is that the mixing time of the chain is usually unknown, which makes it impossible to determine how close the output samples are to having the target distribution. The authors present a novel protocol, the randomness recycler (RR), that… 

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References

SHOWING 1-10 OF 21 REFERENCES

Exact sampling with coupled Markov chains and applications to statistical mechanics

TLDR
This work describes 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, and uses couplings which have also played a role in other sampling schemes.

Exact sampling and approximate counting techniques

  • M. Huber
  • Computer Science, Mathematics
    STOC '98
  • 1998
TLDR
This work presents two algorithms for uniformly sampling from the proper colorings of a graph using colors using the Potts model, and presents the first polynomial time exact sampling algorithm for this problem, which is the first to run in polynometric time.

Fast convergence of the Glauber dynamics for sampling independent sets

TLDR
This paper proves complementary hardness of approximation results, which show that it is hard to sample from this distribution when > c for a constant c > 0 and shows fast convergence of this dynamics.

The Swendsen-Wang process does not always mix rapidly

TLDR
It is shown that there are occasions when the mixing time of the Swendsen–Wang process is exponential in the size of the system, related to the phenomenon of first-order phase transitions in Potts systems with q > 2 states.

On Markov Chains for Independent Sets

TLDR
A new rapidly mixing Markov chain for independent sets is defined and a polynomial upper bound for the mixing time of the new chain is obtained for a certain range of values of the parameter ?, which is wider than the range for which the mixingTime of the Luby?Vigoda chain is known to be polynomially bounded.

The Swendsen–Wang Process Does Not Always Mix Rapidly

The Swendsen–Wang process provides one possible dynamics for the q-state Potts model. Computer simulations of this process are widely used to estimate the expectations of various observables (random

Sampling spin configurations of an Ising system

TLDR
This work shows that by using the JS algorithm and a third equivalent representation of the Ising partition function (the Fortuin-Kasteleyn `random-cluster model’), self-reducibility yields a (classical) polynomial time algorithm for sampling Ising spin configurations.

Amortized efficiency of list update and paging rules

TLDR
This article shows that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules, and analyzes the amortized complexity of LRU, showing that its efficiency differs from that of the off-line paging rule by a factor that depends on the size of fast memory.

Loss networks

TLDR
The model presents questions of call acceptance and capacity allocation (for example, routing), with the aim of ensuring good network performance which is additionally robust with respect to variations in network parameters.