Related papers: On Enumerating Distributions for Associated Vector…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
We consider a novel challenge: approximating a distribution without the ability to randomly sample from that distribution. We study how such an approximation can be obtained using *weight queries*. Given some data set of examples, a weight…
Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: a node-indexed vector has to be reconstructed from measurements of differences between neighbor…
In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…
Potentially influential spaces in the spatial networks of cities can be detected by means of the entropy participation ratios. Local (connectivity) and global (centrality) entropies are considered. While the connectivity entropy has a…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
The paper deals with the distributed minimum sharing problem: a set of decision-makers compute the minimum of some local quantities of interest in a distributed and decentralized way by exchanging information through a communication…
Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…
Using follower/predecessor/extender set sequences, we define quantities which we call the follower/predecessor/extender entropies, which can be associated to any shift space. We analyze the behavior of these quantities under conjugacies and…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
Mixture distributions arise in many parametric and non-parametric settings -- for example, in Gaussian mixture models and in non-parametric estimation. It is often necessary to compute the entropy of a mixture, but, in most cases, this…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Minimum-entropy coupling (MEC) -- the process of finding a joint distribution with minimum entropy for given marginals -- has applications in areas such as causality and steganography. However, existing algorithms are either computationally…
Current approaches to learning vector representations of text that are compatible between different languages usually require some amount of parallel text, aligned at word, sentence or at least document level. We hypothesize however, that…
While the problem of approximate nearest neighbor search has been well-studied for Euclidean space and $\ell_1$, few non-trivial algorithms are known for $\ell_p$ when ($2 < p < \infty$). In this paper, we revisit this fundamental problem…
We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…