Corpus ID: 88515621

# An optimal $(\epsilon,\delta)$-approximation scheme for the mean of random variables with bounded relative variance

@article{Huber2017AnO,
title={An optimal \$(\epsilon,\delta)\$-approximation scheme for the mean of random variables with bounded relative variance},
author={Mark Huber},
journal={arXiv: Computation},
year={2017}
}
• Mark Huber
• Published 2017
• Mathematics
• arXiv: Computation
• Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random variables $X_1,X_2,\ldots$ with finite mean $\mu$ and standard deviation$\sigma$ such that $\mu$ is the solution for the problem input, and the relative standard deviation $|\sigma/\mu| \leq c$ for known $c$. Under these circumstances, it is known that the number of… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 25 REFERENCES

## Approximation algorithms for the normalizing constant of Gibbs distributions

VIEW 1 EXCERPT

## Adaptive Simulated Annealing: A Near-optimal Connection between Sampling and Counting

• Mathematics, Computer Science
• FOCS
• 2007
VIEW 1 EXCERPT

## Loss Minimization and Parameter Estimation with Heavy Tails

• Mathematics, Computer Science
• J. Mach. Learn. Res.
• 2016
VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

## Heavy-tailed regression with a generalized median-of-means

• Computer Science, Mathematics
• ICML
• 2014
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

## Random walks and an O * ( n 5 ) volume algorithm for convex bodies

• Mathematics
• 1997
VIEW 1 EXCERPT

## Faster random generation of linear extensions

• Mathematics, Computer Science
• SODA '98
• 1998
VIEW 1 EXCERPT

## Challenging the empirical mean and empirical variance: a deviation study

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Polynomial-Time Approximation Algorithms for the Ising Model

• Computer Science, Mathematics
• SIAM J. Comput.
• 1993
VIEW 2 EXCERPTS

## Fast perfect sampling from linear extensions

• Mark Huber
• Computer Science, Mathematics
• Discret. Math.
• 2006
VIEW 2 EXCERPTS

## Random Generation of Combinatorial Structures from a Uniform Distribution

• Mathematics, Computer Science
• Theor. Comput. Sci.
• 1986
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL