Related papers: On the randomness of independent experiments
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
Given a collection of probability distributions $p_{1},\ldots,p_{m}$, the minimum entropy coupling is the coupling $X_{1},\ldots,X_{m}$ ($X_{i}\sim p_{i}$) with the smallest entropy $H(X_{1},\ldots,X_{m})$. While this problem is known to be…
Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…