Related papers: Estimation of subgraph density in noisy networks
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Network method of moments arXiv:1202.5101 is an important tool for nonparametric network inference. However, there has been little investigation on accurate descriptions of the sampling distributions of network moment statistics. In this…
Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…
Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate…
Uncertainty quantification has become an important factor in understanding the data representations produced by Graph Neural Networks (GNNs). Despite their predictive capabilities being ever useful across industrial workspaces, the inherent…
We extend the well-known $\beta$-model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel-smoothed likelihood approach for estimating $2n$…
This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for the multiway algorithmic subsample…
Let d = (d1, d2, ..., dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph.…
Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
Graph Neural Networks (GNNs) are a predominant method for graph representation learning. However, beyond subgraph frequency estimation, their application to network motif significance-profile (SP) prediction remains under-explored, with no…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
We consider how to connect a set of disjoint networks to optimize the performance of the resulting composite network. We quantify this performance by the coherence of the composite network, which is defined by an $H_2$ norm of the system.…
For a multi-agent system state estimation resting upon noisy measurements constitutes a problem related to several application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized) analytic…
Deep Learning (DL) holds great promise in reshaping the industry owing to its precision, efficiency, and objectivity. However, the brittleness of DL models to noisy and out-of-distribution inputs is ailing their deployment in sensitive…
Bootstrapping is often applied to get confidence limits for semiparametric inference of a target parameter in the presence of nuisance parameters. Bootstrapping with replacement can be computationally expensive and problematic when…
For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The…
Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…
Recent works have impressively demonstrated that there exists a subnetwork in randomly initialized convolutional neural networks (CNNs) that can match the performance of the fully trained dense networks at initialization, without any…