Related papers: Separating Structure from Noise in Large Graphs Us…

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…

We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological…

In a recent paper, Chernikov and Starchenko prove that graphs defined in distal theories have strong regularity properties, generalizing previous results about graphs defined by semi-algebraic relations. We give a shorter, purely…

It is very common to face classification problems where the number of available labeled samples is small compared to their dimension. These conditions are likely to cause underdetermined settings, with high risk of overfitting. To improve…

The goal of video summarization is to select keyframes that are visually diverse and can represent a whole story of an input video. State-of-the-art approaches for video summarization have mostly regarded the task as a frame-wise keyframe…

Graph similarity search algorithms usually leverage the structural properties of a database. Hence, these algorithms are effective only on some structural variations of the data and are ineffective on other forms, which makes them hard to…

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…

Graph representation learning, involving both node features and graph structures, is crucial for real-world applications but often encounters pervasive noise. State-of-the-art methods typically address noise by focusing separately on node…

Learning a smooth graph signal from partially observed data is a well-studied task in graph-based machine learning. We consider this task from the perspective of optimal recovery, a mathematical framework for learning a function from…

Graph Structure Learning (GSL) focuses on capturing intrinsic dependencies and interactions among nodes in graph-structured data by generating novel graph structures. Graph Neural Networks (GNNs) have emerged as promising GSL solutions,…

Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…

Rule learning approaches for knowledge graph completion are efficient, interpretable and competitive to purely neural models. The rule aggregation problem is concerned with finding one plausibility score for a candidate fact which was…

Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…

Pre-trained language models are increasingly being used in multi-document summarization tasks. However, these models need large-scale corpora for pre-training and are domain-dependent. Other non-neural unsupervised summarization approaches…

Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

Dividing asks about inconsistency along indiscernible sequences. In order to study the finer structure of simple theories without much dividing, the authors recently introduced shearing, which essentially asks about inconsistency along…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the…