English
Related papers

Related papers: The probability of drawing intersections: extendin…

200 papers

We consider a problem of data integration. Consider determining which genes affect a disease. The genes, which we call predictor objects, can be measured in different experiments on the same individual. We address the question of finding…

Machine Learning · Statistics 2016-10-04 Xin Gao , Raymond J. Carroll

We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…

Probability · Mathematics 2021-11-01 Suqi Liu , Miklos Z. Racz

The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…

Probability · Mathematics 2023-09-07 Paulo Manrique-Mirón

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…

Machine Learning · Computer Science 2020-10-30 Shib Sankar Dasgupta , Michael Boratko , Dongxu Zhang , Luke Vilnis , Xiang Lorraine Li , Andrew McCallum

Given two weighted k-uniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of…

Combinatorics · Mathematics 2014-08-28 Béla Bollobás , Alex Scott

An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this probability distribution where $N$ may be…

Statistics Theory · Mathematics 2016-09-29 Anna Ben-Hamou , Stéphane Boucheron , Mesrob I. Ohannessian

A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…

Methodology · Statistics 2024-07-11 Anupama Nandi , Subrata Chakraborty , Aniket Biswas

A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…

Probability · Mathematics 2015-09-24 Maria Deijfen , Willemien Kets

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…

Statistical Mechanics · Physics 2009-11-10 Bo Söderberg

We study the connections between the notions of combinatorial discrepancy and graph degeneracy. In particular, we prove that the maximum discrepancy over all subgraphs $H$ of a graph $G$ of the neighborhood set system of $H$ is sandwiched…

Discrete Mathematics · Computer Science 2021-11-30 Mario Grobler , Yiting Jiang , Patrice Ossona de Mendez , Sebastian Siebertz , Alexandre Vigny

We present new sampling methods in finite population that allow to control the joint inclusion probabilities of units and especially the spreading of sampled units in the population. They are based on the use of renewal chains and…

Methodology · Statistics 2017-04-12 Yves Tillé , Lionel Qualité , Matthieu Wilhelm

Suppose that there is a family of $n$ random points $X_v$ for $v \in V$, independently and uniformly distributed in the square $\left[-\sqrt{n}/2,\sqrt{n}/2\right]^2$ of area $n$. We do not see these points, but learn about them in one of…

Probability · Mathematics 2019-11-26 Josep Diaz , Colin McDiarmid , Dieter Mitsche

We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…

Soft Condensed Matter · Physics 2020-10-29 Lucas Böttcher

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

Information Theory · Computer Science 2018-01-16 Mihai-Alin Badiu , Justin P. Coon

Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of…

Machine Learning · Statistics 2010-07-16 Sergey M. Plis , Terran Lane , Vince D. Calhoun

We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique…

Combinatorics · Mathematics 2010-04-27 Jacob Fox , Benny Sudakov

Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…

Machine Learning · Computer Science 2024-03-06 Jianan Fan , Dongnan Liu , Hang Chang , Heng Huang , Mei Chen , Weidong Cai

We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…

Machine Learning · Statistics 2023-07-03 Amir Asiaee , Samet Oymak , Kevin R. Coombes , Arindam Banerjee

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

Statistics Theory · Mathematics 2025-10-07 Henrik Kaiser

Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…

Information Theory · Computer Science 2018-10-16 Sara Shahi , Daniela Tuninetti , Natasha Devroye