Related papers: A generalization of the Von Neumann extractor
In this article, we study a notion of the extraction rate of Turing functionals that translate between notions of randomness with respect to different underlying probability measures. We analyze several classes of extraction procedures: a…
We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric…
Peres algorithm applies the famous von Neumann trick recursively to produce unbiased random bits from biased coin tosses. Its recursive nature makes the algorithm simple and elegant, and yet its output rate approaches the…
An algorithm is presented that, taking a sequence of independent Bernoulli random variables with parameter $1/2$ as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter $\tau$.…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
This article presents an efficient algorithm to generate a discrete uniform distribution on a set of $p$ elements using a biased random source for $p$ prime. The algorithm generalizes Von Neumann's method and improves computational…
Given a known function $f : [0, 1] \mapsto (0, 1)$ and a random but almost surely finite number of independent, Ber$(x)$-distributed random variables with unknown $x \in [0, 1]$, we construct an unbiased, $[0, 1]$-valued estimator of the…
Thevon Neumann entropy, named after John von Neumann, is an extension of the classical concept of entropy to the field of quantum mechanics. From a numerical perspective, von Neumann entropy can be computed simply by computing all…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
The toss of a coin is usually regarded as the epitome of randomness, and has been used for ages as a means to resolve disputes in a simple, fair way. Perhaps as ancient as consulting objects such as coins and dice is the art of maliciously…
The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute…
The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…
We investigate a population of binary mistake sequences that result from learning with parametric models of different order. We obtain estimates of their error, algorithmic complexity and divergence from a purely random Bernoulli sequence.…
In this paper, an analysis of the undetected error probability of ensembles of binary matrices is presented. The ensemble called the Bernoulli ensemble whose members are considered as matrices generated from i.i.d. Bernoulli source is…
A Bernoulli factory is a model for randomness manipulation that transforms an initial Bernoulli random variable into another Bernoulli variable by applying a predetermined function relating the output bias to the input one. In literature,…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…
The Bernoulli Factory is an algorithm that takes as input a series of i.i.d. Bernoulli random variables with an unknown but fixed success probability $p$, and outputs a corresponding series of Bernoulli random variables with success…
We introduce a theory of probabilistic renormalization for series, the renormalized values being encoded in the expectation of a certain random variable on the set of natural numbers. We identify a large class of weakly renormalizable…
In the note we consider an iterative generalisation of the rejection sampling method. In high energy physics, this sampling is frequently used for event generation, i.e. preparation of phase space points distributed according to a matrix…