相关论文: Optimal Adaptivity of Signed-Polygon Statistics fo…

We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…

The problem of finding overlapping communities in networks has gained much attention recently. Optimization-based approaches use non-negative matrix factorization (NMF) or variants, but the global optimum cannot be provably attained in…

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…

Graph Neural Networks (GNNs) have demonstrated impressive performance across diverse graph-based tasks by leveraging message passing to capture complex node relationships. However, on large-scale real-world graphs, GNNs face two major…

Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…

Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…

In this paper we study the random geometric graph $\mathsf{RGG}(n,\mathbb{T}^d,\mathsf{Unif},\sigma^q_p,p)$ with $L_q$ distance where each vertex is sampled uniformly from the $d$-dimensional torus and where the connection radius is chosen…

How can researchers test for heterogeneity in the local structure of a network? In this paper, we present a framework that utilizes random sampling to give subgraphs which are then used in a goodness of fit test to test for heterogeneity.…

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…

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including…

Complex networks considering both positive and negative links have gained considerable attention during the past several years. Community detection is one of the main challenges for complex network analysis. Most of the existing algorithms…

Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…

We investigate signed networks with community structure with respect to their spectrum and their evolution under a dynamical model of structural balance, a prominent theory of signed social networks. The spectrum of the adjacency matrix…

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…

We consider the problem of detecting sparse heterogeneous mixtures from a nonparametric perspective, and develop distribution-free tests when all effects have the same sign. Specifically, we assume that the null distribution is symmetric…

In this work, we consider the sparsity-constrained community-based group testing problem, where the population follows a community structure. In particular, the community consists of $F$ families, each with $M$ members. A number $k_f$ out…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

We introduce Selective Greedy Equivalence Search (SGES), a restricted version of Greedy Equivalence Search (GES). SGES retains the asymptotic correctness of GES but, unlike GES, has polynomial performance guarantees. In particular, we show…

We are interested in the problem of two-sample network hypothesis testing: given two networks with the same set of nodes, we wish to test whether the underlying Bernoulli probability matrices of the two networks are the same or not. We…

Graphs are ubiquitous for modeling complex systems involving structured data and relationships. Consequently, graph representation learning, which aims to automatically learn low-dimensional representations of graphs, has drawn a lot of…