Related papers: When is Nontrivial Estimation Possible for Graphon…

In this paper we analyze the necessary number of samples to estimate the gradient of any multidimensional smooth (possibly non-convex) function in a zero-order stochastic oracle model. In this model, an estimator has access to noisy values…

Consider a pair of sparse correlated stochastic block models $\mathcal S(n,\tfrac{\lambda}{n},\epsilon;s)$ subsampled from a common parent stochastic block model with two symmetric communities, average degree $\lambda=O(1)$, divergence…

Graph sketching is a powerful paradigm for analyzing graph structure via linear measurements introduced by Ahn, Guha, and McGregor (SODA'12) that has since found numerous applications in streaming, distributed computing, and massively…

The study of adaptive data analysis examines how many statistical queries can be answered accurately using a fixed dataset while avoiding false discoveries (statistically inaccurate answers). In this paper, we tackle a question that…

Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…

We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for…

In the theory of dense graph limits, a graphon is a symmetric measurable function $W:[0,1]^2\to [0,1]$. Each graphon gives rise naturally to a random graph distribution, denoted $\mathbb{G}(n,W)$, that can be viewed as a generalization of…

The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with…

Random graph mixture models are now very popular for modeling real data networks. In these setups, parameter estimation procedures usually rely on variational approximations, either combined with the expectation-maximisation (\textsc{em})…

$\Theta_6$-Graphs graphs are important geometric graphs that have many applications especially in wireless sensor networks. They are equivalent to Delaunay graphs where empty equilateral triangles take the place of empty circles. We…

Biclustering structures in data matrices were first formalized in a seminal paper by John Hartigan (1972) where one seeks to cluster cases and variables simultaneously. Such structures are also prevalent in block modeling of networks. In…

Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified…

High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it…

Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…

The celebrated theorem of Chung, Graham, and Wilson on quasirandom graphs implies that if the 4-cycle and edge counts in a graph $G$ are both close to their typical number in $\mathbb{G}(n,1/2),$ then this also holds for the counts of…

We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…

Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called \textit{graphon autoencoder} to build an interpretable…