Related papers: Multiparameter Bernoulli Factories
Randomness processing in the Bernoulli factory framework provides a concrete setting in which quantum resources can outperform classical ones. We experimentally demonstrate an entanglement-assisted quantum Bernoulli factory based on…
In this paper, we systematize the modeling of probabilistic systems for the purpose of analyzing them with model counting techniques. Starting from unbiased coin flips, we show how to model biased coins, correlated coins, and distributions…
We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
Probabilistic artificial neural networks offer intriguing prospects for enabling the uncertainty of artificial intelligence methods to be described explicitly in their function; however, the development of techniques that quantify…
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.…
We consider $N$ Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion $L_N$ of variables in a given…
Let $q \in (0,1)$ and $\delta \in (0,1)$ be real numbers, and let $C$ be a coin that comes up heads with an unknown probability $p$, such that $p \neq q$. We present an algorithm that, on input $C$, $q$, and $\delta$, decides, with…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…
A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case.…
A function defined on the Boolean hypercube is $k$-Fourier-sparse if it has at most $k$ nonzero Fourier coefficients. For a function $f: \mathbb{F}_2^n \rightarrow \mathbb{R}$ and parameters $k$ and $d$, we prove a strong upper bound on the…
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…
Difficult it is to formulate achievable sensitivity bounds for quantum multiparameter estimation. Consider a special case, one parameter from many: many parameters of a process are unknown; estimate a specific linear combination of these…
Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be…
We study a functional equation whose unknown maps a Euclidean space into the space of probability distributions on [0,1]. We prove existence and uniqueness of its solution under suitable regularity and boundary conditions, we show that it…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for…