Related papers: Estimating Entropy of Distributions in Constant Sp…
We observe an infinite sequence of independent identically distributed random variables $X_1,X_2,\ldots$ drawn from an unknown distribution $p$ over $[n]$, and our goal is to estimate the entropy $H(p)=-\mathbb{E}[\log p(X)]$ within an…
We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-\epsilon$. It is shown that every randomized streaming algorithm for this problem needs space $\Omega(\log n + \log b -…
We consider the problem of approximating the empirical Shannon entropy of a high-frequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is…
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,…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
We present an $O((\log k)^2)$-competitive randomized algorithm for the $k$-server problem on hierarchically separated trees (HSTs). This is the first $o(k)$-competitive randomized algorithm for which the competitive ratio is independent of…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
The random order graph streaming model has received significant attention recently, with problems such as matching size estimation, component counting, and the evaluation of bounded degree constant query testable properties shown to admit…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
Estimating statistical properties is fundamental in statistics and computer science. In this paper, we propose a unified quantum algorithm framework for estimating properties of discrete probability distributions, with estimating R\'enyi…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
We initiate a study of the following problem: Given a continuous domain $\Omega$ along with its convex hull $\mathcal{K}$, a point $A \in \mathcal{K}$ and a prior measure $\mu$ on $\Omega$, find the probability density over $\Omega$ whose…
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…
Histograms, i.e., piece-wise constant approximations, are a popular tool used to represent data distributions. Traditionally, the difference between the histogram and the underlying distribution (i.e., the approximation error) is measured…
We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and…
Compression of documents, images, audios and videos have been traditionally practiced to increase the efficiency of data storage and transfer. However, in order to process or carry out any analytical computations, decompression has become…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…