Related papers: Local weak convergence and its applications

PageRank is a well-known algorithm for measuring centrality in networks. It was originally proposed by Google for ranking pages in the World-Wide Web. One of the intriguing empirical properties of PageRank is the so-called `power-law…

(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary…

The main goal of this paper is twofold. First, we extend some results known in the case of weak greedy algorithms with a scalar parameter to the case of weak greedy algorithms with a weakness sequence. Second, we formulate a new setting of…

Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…

Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a…

As an emerging and challenging problem in the computer vision community, weakly supervised object localization and detection plays an important role for developing new generation computer vision systems and has received significant…

In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…

Learning the right graph representation from noisy, multi-source data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information…

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

We use an inequality of Sidorenko to show a general relation between local and global subgraph counts and degree moments for locally weakly convergent sequences of sparse random graphs. This yields an optimal criterion to check when the…

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…

Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…

The weak-to-strong generalization phenomenon is the driver for important machine learning applications including highly data-efficient learning and, most recently, performing superalignment. While decades of research have resulted in…

In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover,…

A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…

Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…

The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of…

Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey…