
Stationarity in the Realizations of the Causal RateDistortion Function for OneSided Stationary Sources
This paper derives novel results on the characterization of the the caus...
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An Orthogonality Principle for SelectMaximum Estimation of Exponential Variables
It was recently proposed to encode the onesided exponential source X in...
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FPRAS for the Potts Model and the Number of kcolorings
In this paper, we give a sampling algorithm for the Potts model using Ma...
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Rademacher complexity for Markov chains : Applications to kernel smoothing and MetropolisHasting
Following the seminal approach by Talagrand, the concept of Rademacher c...
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On the Uniqueness of Simultaneous Rational Function Reconstruction
This paper focuses on the problem of reconstructing a vector of rational...
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Combinatorial Bernoulli Factories: Matchings, Flows and Other Polytopes
A Bernoulli factory is an algorithmic procedure for exact sampling of ce...
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Signaling Games for Arbitrary Distributions: Number of Bins and Properties of Equilibria
We investigate the equilibrium behavior for the decentralized quadratic ...
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From the Bernoulli Factory to a Dice Enterprise via Perfect Sampling of Markov Chains
Given a pcoin that lands heads with unknown probability p, we wish to produce an f(p)coin for a given function f: (0,1) → (0,1). This problem is commonly known as the Bernoulli Factory and results on its solvability and complexity have been obtained in <cit.>. Nevertheless, generic ways to design a practical Bernoulli Factory for a given function f exist only in a few special cases. We present a constructive way to build an efficient Bernoulli Factory when f(p) is a rational function with coefficients in R. Moreover, we extend the Bernoulli Factory problem to a more general setting where we have access to an msided die and we wish to roll a vsided one; i.e., we consider rational functions f: Δ^m1→Δ^v1 between open probability simplices. Our construction consists of rephrasing the original problem as simulating from the stationary distribution of a certain class of Markov chains  a task that we show can be achieved using perfect simulation techniques with the original msided die as the only source of randomness. In the Bernoulli Factory case, the number of tosses needed by the algorithm has exponential tails and its expected value can be bounded uniformly in p. En route to optimizing the algorithm we show a fact of independent interest: every finite, integer valued, random variable will eventually become logconcave after convolving with enough Bernoulli trials.
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