Related papers: Limit Theorems for Network Dependent Random Variab…
We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…
We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected…
An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics.…
We propose a novel class of separable multilayer network models to capture cross-layer dependencies in multilayer networks, enabling the analysis of how interactions in one or more layers may influence interactions in other layers. Our…
Differences between biological networks corresponding to disease conditions can help delineate the underlying disease mechanisms. Existing methods for differential network analysis do not account for dependence of networks on covariates. As…
This paper develops the sufficiency principle suitable for data reduction in decentralized inference systems. Both parallel and tandem networks are studied and we focus on the cases where observations at decentralized nodes are…
We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the mean-field of the afferent edges and nodes. The flipping of…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include $n$ agents, whose opinions are given by latent stochastic processes,…
Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often naive to assume that the underlying…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…