Related papers: New Tests of Randomness for Circular Data
Randomness or mutual independence is a fundamental assumption forming the basis of statistical inference across disciplines such as economics, finance, and management. Consequently, validating this assumption is essential for the reliable…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
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…
We consider random graphs in which the edges are allowed to be dependent. In our model the edge dependence is quite general, we call it $p$-robust random graph. It means that every edge is present with probability at least $p$, regardless…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
We initiate the study of distribution testing for probability distributions over the edges of a graph, motivated by the closely related question of ``edge-distribution-free'' graph property testing. The main results of this paper are…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
Graph data has a unique structure that deviates from standard data assumptions, often necessitating modifications to existing methods or the development of new ones to ensure valid statistical analysis. In this paper, we explore the notion…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…
In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated. For a given undirected graph $G$, the network failure probability is the probability that…
Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
In this thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\ldots X_{n},Y_{1},\ldots Y_{n}$ be $2n$ independent random variables, with uniform…
We study high-dimensional random geometric graphs (RGGs) of edge-density $p$ with vertices uniformly distributed on the $d$-dimensional torus and edges inserted between sufficiently close vertices with respect to an $L_q$-norm. We focus on…