Related papers: Distance Distribution Between Two Random Nodes in …
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
Let $\mathbf{H}=(h_{ij})$ and $\mathbf{G}=(g_{ij})$ be two $m\times n$, $m\leq n$, random matrices, each with i.i.d complex zero-mean unit-variance Gaussian entries, with correlation between any two elements given by…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions and…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
The information that can be transmitted through a wireless channel, with multiple-antenna equipped transmitter and receiver, is crucially influenced by the channel behavior as well as by the structure of the input signal. We characterize in…
I propose a method to fit the probability distribution function (hereafter PDF) of the large scale density field rho, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
We apply a recent one-dimensional algorithm for predicting random close packing fractions of polydisperse hard spheres [Farr and Groot, J. Chem. Phys. 133, 244104 (2009)] to the case of lognormal distributions of sphere sizes and mixtures…
The statistical characterization of the sum of random variables (RVs) are useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and…
Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no…
We develop a formalism to describe the equilibrium distributions for segments of confined branched networks consisting of stiff filaments. This is applicable to certain situations of cytoskeleton in cells, such as for example actin…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
We propose a simple stochastic model describing the position-dependent ball-passing network in football games. In this network, a player on a certain area in the divided fields is a node, and a pass between two nodes corresponds to an edge.…