Related papers: Two-sample Hypothesis Testing for Inhomogeneous Ra…
A graph $G$ is $q$-Ramsey for another graph $H$ if in any $q$-edge-colouring of $G$ there is a monochromatic copy of $H$, and the classic Ramsey problem asks for the minimum number of vertices in such a graph. This was broadened in the…
Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block…
Lov\'asz (1967) showed that two graphs $G$ and $H$ are isomorphic if, and only if, they are homomorphism indistinguishable over all graphs, i.e., $G$ and $H$ admit the same number of number of homomorphisms from every graph $F$.…
In clinical and neuroscientific studies, systematic differences between two populations of brain networks are investigated in order to characterize mental diseases or processes. Those networks are usually represented as graphs built from…
This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and…
In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
This paper addresses the multiple two-sample test problem in a graph-structured setting, which is a common scenario in fields such as Spatial Statistics and Neuroscience. Each node $v$ in fixed graph deals with a two-sample testing problem…
Network data is a major object data type that has been widely collected or derived from common sources such as brain imaging. Such data contains numeric, topological, and geometrical information, and may be necessarily considered in certain…
We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…
In many statistical applications, the dimension is too large to handle for standard high-dimensional machine learning procedures. This is particularly true for graphical models, where the interpretation of a large graph is difficult and…
In this work, we look at a two-sample problem within the framework of Gaussian graphical models. When the global hypothesis of equality of two distributions is rejected, the interest is usually in localizing the source of difference.…
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…
We study the problem of two-sample comparison with categorical data when the contingency table is sparsely populated. In modern applications, the number of categories is often comparable to the sample size, causing existing methods to have…
Testing equality of two multivariate distributions is a classical problem for which many non-parametric tests have been proposed over the years. Most of the popular two-sample tests, which are asymptotically distribution-free, are based…
We propose the use of non-parametric, graph-based tests to assess the distributional balance of covariates in observational studies with multi-valued treatments. Our tests utilize graph structures ranging from Hamiltonian paths that connect…
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
In the regime of two-sample comparison, tests based on a graph constructed on observations by utilizing similarity information among them is gaining attention due to their flexibility and good performances for high-dimensional/non-Euclidean…
Many complex networks in real world can be formulated as hypergraphs where community detection has been widely used. However, the fundamental question of whether communities exist or not in an observed hypergraph still remains unresolved.…