Related papers: Model-free consistency of graph partitioning
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
For random graphs distributed according to a stochastic block model, we consider the inferential task of partioning vertices into blocks using spectral techniques. Spectral partioning using the normalized Laplacian and the adjacency matrix…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…
Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
We investigate various forms of (model-theoretic) stability for hypergraphs and their corresponding strengthenings of the hypergraph regularity lemma with respect to partitions of vertices. On the one hand, we provide a complete…
We consider the problem of learning the structure of ferromagnetic Ising models Markov on sparse Erdos-Renyi random graph. We propose simple local algorithms and analyze their performance in the regime of correlation decay. We prove that an…
Causal modeling has long been an attractive topic for many researchers and in recent decades there has seen a surge in theoretical development and discovery algorithms. Generally discovery algorithms can be divided into two approaches:…
Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…
Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
Traditional statistical learning theory relies on the assumption that data are identically and independently distributed (i.i.d.). However, this assumption often does not hold in many real-life applications. In this survey, we explore…
In the present paper a novel graph-based approach to the shape decomposition problem is addressed. The shape is appropriately transformed into a visibility graph enriched with local neighborhood information. A two-step diffusion process is…
Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and…
Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as…