Related papers: A PAC-Bayesian Approach to Generalization Bounds f…
Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed…
Analysing statistical properties of neural networks is a central topic in statistics and machine learning. However, most results in the literature focus on the properties of the neural network minimizing the training error. The goal of this…
Graph Neural Networks (GNNs) have become a popular approach for various applications, ranging from social network analysis to modeling chemical properties of molecules. While GNNs often show remarkable performance on public datasets, they…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between…
Graph Neural Networks (GNNs) are increasingly becoming the favorite method for graph learning. They exploit the semi-supervised nature of deep learning, and they bypass computational bottlenecks associated with traditional graph learning…
We investigate adaptive layer-wise graph convolution in deep GCN models. We propose AdaGPR to learn generalized Pageranks at each layer of a GCNII network to induce adaptive convolution. We show that the generalization bound for AdaGPR is…
We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and…
We propose a graph semi-supervised learning framework for classification tasks on data manifolds. Motivated by the manifold hypothesis, we model data as points sampled from a low-dimensional manifold $\mathcal{M} \subset \mathbb{R}^F$. The…
Aggregated predictors are obtained by making a set of basic predictors vote according to some weights, that is, to some probability distribution. Randomized predictors are obtained by sampling in a set of basic predictors, according to some…
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…
A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas…
This paper proposes a generalized Mundlak estimator based on graph neural networks (GME-GNN). The estimator is designed to mitigate bias arising from group-level heterogeneity and to accommodate within-group dependence among individuals.…
There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width. However, these results do not…
Graph Neural Networks (GNN) have emerged as a popular and standard approach for learning from graph-structured data. The literature on GNN highlights the potential of this evolving research area and its widespread adoption in real-life…
Graph neural networks (GNNs), as the de-facto model class for representation learning on graphs, are built upon the multi-layer perceptrons (MLP) architecture with additional message passing layers to allow features to flow across nodes.…
Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been…
Due to the fact much of today's data can be represented as graphs, there has been a demand for generalizing neural network models for graph data. One recent direction that has shown fruitful results, and therefore growing interest, is the…