Related papers: New Tests of Randomness for Circular Data
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…
Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…
We consider the ergodicity and consensus problem for a discrete-time linear dynamic model driven by random stochastic matrices, which is equivalent to studying these concepts for the product of such matrices. Our focus is on the model where…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its…
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…
The assumption that data samples are independent and identically distributed (iid) is standard in many areas of statistics and machine learning. Nevertheless, in some settings, such as social networks, infectious disease modeling, and…
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
Recently, Anderson et al. (2019) proposed the concept of rankability, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. In the same paper, they proposed a rankability measure that is based on a…