Related papers: Detecting Correlation between Multiple Unlabeled G…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
The tau constant is an important invariant of a metrized graph, and it has applications in arithmetic properties of curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We…
We consider the classical Neymann-Pearson hypothesis testing problem of signal detection, where under the null hypothesis ($\calH_0$), the received signal is white Gaussian noise, and under the alternative hypothesis ($\calH_1$), the…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
Understanding the correlation between two different scores for the same set of items is a common problem in information retrieval, and the most commonly used statistics that quantifies this correlation is Kendall's $\tau$. However, the…
A good edge-labeling of a graph [Ara\'ujo, Cohen, Giroire, Havet, Discrete Appl. Math., forthcoming] is an assignment of numbers to the edges such that for no pair of vertices, there exist two non-decreasing paths. In this paper, we study…
In this work, we propose an efficient two-stage algorithm solving a joint problem of correlation detection and partial alignment recovery between two Gaussian databases. Correlation detection is a hypothesis testing problem; under the null…
We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…
We consider the problem of late change-point detection under the preferential attachment random graph model with time dependent attachment function. This can be formulated as a hypothesis testing problem where the null hypothesis…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
A graph $G = (V,E)$ is a double-threshold graph if there exist a vertex-weight function $w \colon V \to \mathbb{R}$ and two real numbers $\mathtt{lb}, \mathtt{ub} \in \mathbb{R}$ such that $uv \in E$ if and only if $\mathtt{lb} \le…
Uncover the vertices of a given graph, deterministic or random, in random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization…
We introduce a new model of correlated randomly growing graphs and study the fundamental questions of detecting correlation and estimating aspects of the correlated structure. The model is simple and starts with any model of randomly…
A matching $M$ in a graph $G$ is {\em connected} if $G$ has an edge linking each pair of edges in $M$. The problem to find large connected matchings in graphs $G$ with $\alpha(G)=2$ is closely related to Hadwiger's conjecture for graphs…
Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields. Parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models. In this paper, we study a…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
Zhu et al. [Theoret. Comput. Sci. 758 (2019) 1--8] introduced the $h$-edge tolerable diagnosability to measure the fault diagnosis capability of a multiprocessor system with faulty links. This kind of diagnosability is a generalization of…