1,386,377 research outputs found
Sampling Random Colorings of Sparse Random Graphs
We study the mixing properties of the single-site Markov chain known as the
Glauber dynamics for sampling -colorings of a sparse random graph
for constant . The best known rapid mixing results for general graphs are in
terms of the maximum degree of the input graph and hold when
for all . Improved results hold when for
graphs with girth and sufficiently large where is the root of ; further improvements on
the constant hold with stronger girth and maximum degree assumptions.
For sparse random graphs the maximum degree is a function of and the goal
is to obtain results in terms of the expected degree . The following rapid
mixing results for hold with high probability over the choice of the
random graph for sufficiently large constant~. Mossel and Sly (2009) proved
rapid mixing for constant , and Efthymiou (2014) improved this to linear
in~. The condition was improved to by Yin and Zhang (2016) using
non-MCMC methods. Here we prove rapid mixing when where
is the same constant as above. Moreover we obtain
mixing time of the Glauber dynamics, while in previous rapid mixing
results the exponent was an increasing function in . As in previous results
for random graphs our proof analyzes an appropriately defined block dynamics to
"hide" high-degree vertices. One new aspect in our improved approach is
utilizing so-called local uniformity properties for the analysis of block
dynamics. To analyze the "burn-in" phase we prove a concentration inequality
for the number of disagreements propagating in large blocks
Optimal random sampling designs in random field sampling
A Horvitz-Thompson predictor is proposed for spatial sampling when the characteristic of interest is modeled as a random field. Optimal sampling designs are deduced under this context. Fixed and variable sample size are considered
OPTIMAL RANDOM SAMPLING DESIGNS IN RANDOM FIELD SAMPLING
A Horvitz-Thompson predictor is proposed for spatial sampling when the characteristic of interest is modeled as a random field. Optimal sampling designs are deduced under this context. Fixed and variable sample size are considered.
Parallel Weighted Random Sampling
Data structures for efficient sampling from a set of weighted items are an important building block of many applications. However, few parallel solutions are known. We close many of these gaps both for shared-memory and distributed-memory machines. We give efficient, fast, and practicable algorithms for sampling single items, k items with/without replacement, permutations, subsets, and reservoirs. We also give improved sequential algorithms for alias table construction and for sampling with replacement. Experiments on shared-memory parallel machines with up to 158 threads show near linear speedups both for construction and queries
Densities for random balanced sampling
A random balanced sample (RBS) is a multivariate distribution with n
components X_1,...,X_n, each uniformly distributed on [-1, 1], such that the
sum of these components is precisely 0. The corresponding vectors X lie in an
(n-1)-dimensional polytope M(n). We present new methods for the construction of
such RBS via densities over M(n) and these apply for arbitrary n. While simple
densities had been known previously for small values of n (namely 2,3 and 4),
for larger n the known distributions with large support were fractal
distributions (with fractal dimension asymptotic to n as n approaches
infinity). Applications of RBS distributions include sampling with antithetic
coupling to reduce variance, and the isolation of nonlinearities. We also show
that the previously known densities (for n<5) are in fact the only solutions in
a natural and very large class of potential RBS densities. This finding
clarifies the need for new methods, such as those presented here.Comment: 20 pages, 6 figures, to appear in Journal of Multivariate Analysi
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