Related papers: Berry-Esseen bound of modularity in network
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known…
As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically…
A model algorithm is proposed to study subsequent partitions of complex networks describing social structures. The partitions are supposed to appear as actions of rivaling leaders corresponding to nodes with large degrees. The condition of…
We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the dimension of the hyperbolic space is two or general odd. Our…
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
For a series of univariate or multivariate complex multiple Wiener-It\^o integrals, we appreciably improve the previously known contractions condition of complex Fourth Moment Theorem (FMT) and present a fourth moment type Berry-Ess\'een…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying…
An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the…
We prove some new bounds for the size of the maximal dissociated subset of structured (having small sumset, large energy and so on) subsets A of an abelian group.
Based on the density of connections between the nodes of high degree, we introduce two bounds of the spectral radius. We use these bounds to split a network into two sets, one of these sets contains the high degree nodes, we refer to this…
We have analyzed the detectability limits of network communities in the framework of the popular Girvan and Newman benchmark. By carefully taking into account the inevitable stochastic fluctuations that affect the construction of each and…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
A recent result has demonstrated that the Bethe partition function always lower bounds the true partition function of binary, log-supermodular graphical models. We demonstrate that these results can be extended to other interesting classes…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…
For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.
We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of…
A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…
There has been a resurgence of interest in incomplete U-statistics that only sum over a subset of kernel evaluations, due to their computational efficiency and asymptotic normality which can be leveraged to quantify the uncertainty of…