Related papers: Graph-based Generalization Bounds for Learning Bin…

We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties cannot be computed by GNNs that rely entirely on local information. Such GNNs include the standard message…

Graph Neural Networks (GNNs) have achieved notable success in learning from graph-structured data, owing to their ability to capture intricate dependencies and relationships between nodes. They excel in various applications, including…

We present a semi-supervised learning framework based on graph embeddings. Given a graph between instances, we train an embedding for each instance to jointly predict the class label and the neighborhood context in the graph. We develop…

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…

In recent years, several results in the supervised learning setting suggested that classical statistical learning-theoretic measures, such as VC dimension, do not adequately explain the performance of deep learning models which prompted a…

In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…

As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…

We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can…

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted…

Despite enormous successful applications of graph neural networks (GNNs), theoretical understanding of their generalization ability, especially for node-level tasks where data are not independent and identically-distributed (IID), has been…

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…

Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. Over the years, graph learning has transcended from graph theory to graph data mining. With the…

A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i.d. assumption does not hold. We consider learning problems in…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Despite remarkable success in a variety of applications, it is well-known that deep learning can fail catastrophically when presented with out-of-distribution data. Toward addressing this challenge, we consider the domain generalization…

Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic…

We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to…

Graph learning has become essential in various domains, including recommendation systems and social network analysis. Graph Neural Networks (GNNs) have emerged as promising techniques for encoding structural information and improving…

The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep…

Domain generalization is the problem of assigning labels to an unlabeled data set, given several similar data sets for which labels have been provided. Despite considerable interest in this problem over the last decade, there has been no…