Related papers: New Tests of Randomness for Circular Data
We classify isomorphism-invariant random digraphs according to where randomness resides, namely, arcs, vertices, and vertices and arcs together which in turn yield arc random digraphs (ARD), vertex random digraphs (VRD) and vertex-arc…
We present a new method for learning Soft Random Geometric Graphs (SRGGs), drawn in probabilistic metric spaces, with the connection function of the graph defined as the marginal posterior probability of an edge random variable, given the…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
The distribution $\mathsf{RGG}(n,\mathbb{S}^{d-1},p)$ is formed by sampling independent vectors $\{V_i\}_{i = 1}^n$ uniformly on $\mathbb{S}^{d-1}$ and placing an edge between pairs of vertices $i$ and $j$ for which $\langle V_i,V_j\rangle…
Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…
Traditional statistical learning theory relies on the assumption that data are identically and independently distributed (i.i.d.). However, this assumption often does not hold in many real-life applications. In this survey, we explore…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random…
The problem of testing the reliability of ensemble forecasting systems is revisited. A popular tool to assess the reliability of ensemble forecasting systems (for scalar verifications) is the rank histogram, this histogram is expected to be…
Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product…
Independence analysis is an indispensable step before regression analysis to find out essential factors that influence the objects. With many applications in machine Learning, medical Learning and a variety of disciplines, statistical…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
One of the intensely studied concepts of network robustness is $r$-robustness, which is a network topology property quantified by an integer $r$. It is required by mean subsequence reduced (MSR) algorithms and their variants to achieve…
This work addressed the problem of learning a network with communication between vertices. The communication between vertices is presented in the form of perturbation on the measure. We studied the scenario where samples are drawn from a…
It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some unidentifiable similarity transformations. Our test statistic is…
We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…