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Vazirgiannis, Michalis


Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction

arXiv.org Machine Learning

Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as powerful methods for link prediction. Their performances are less impressive on community detection problems where, according to recent and concurring experimental evaluations, they are often outperformed by simpler alternatives such as the Louvain method. It is currently still unclear to which extent one can improve community detection with GAE and VGAE, especially in the absence of node features. It is moreover uncertain whether one could do so while simultaneously preserving good performances on link prediction. In this paper, we show that jointly addressing these two tasks with high accuracy is possible. For this purpose, we introduce and theoretically study a community-preserving message passing scheme, doping our GAE and VGAE encoders by considering both the initial graph structure and modularity-based prior communities when computing embedding spaces. We also propose novel training and optimization strategies, including the introduction of a modularity-inspired regularizer complementing the existing reconstruction losses for joint link prediction and community detection. We demonstrate the empirical effectiveness of our approach, referred to as Modularity-Aware GAE and VGAE, through in-depth experimental validation on various real-world graphs.


Graph Kernels: A Survey

Journal of Artificial Intelligence Research

Graph kernels have attracted a lot of attention during the last decade, and have evolved into a rapidly developing branch of learning on structured data. During the past 20 years, the considerable research activity that occurred in the field resulted in the development of dozens of graph kernels, each focusing on specific structural properties of graphs. Graph kernels have proven successful in a wide range of domains, ranging from social networks to bioinformatics. The goal of this survey is to provide a unifying view of the literature on graph kernels. In particular, we present a comprehensive overview of a wide range of graph kernels. Furthermore, we perform an experimental evaluation of several of those kernels on publicly available datasets, and provide a comparative study. Finally, we discuss key applications of graph kernels, and outline some challenges that remain to be addressed.


Permute Me Softly: Learning Soft Permutations for Graph Representations

arXiv.org Machine Learning

Graph neural networks (GNNs) have recently emerged as a dominant paradigm for machine learning with graphs. Research on GNNs has mainly focused on the family of message passing neural networks (MPNNs). Similar to the Weisfeiler-Leman (WL) test of isomorphism, these models follow an iterative neighborhood aggregation procedure to update vertex representations, and they next compute graph representations by aggregating the representations of the vertices. Although very successful, MPNNs have been studied intensively in the past few years. Thus, there is a need for novel architectures which will allow research in the field to break away from MPNNs. In this paper, we propose a new graph neural network model, so-called $\pi$-GNN which learns a "soft" permutation (i.e., doubly stochastic) matrix for each graph, and thus projects all graphs into a common vector space. The learned matrices impose a "soft" ordering on the vertices of the input graphs, and based on this ordering, the adjacency matrices are mapped into vectors. These vectors can be fed into fully-connected or convolutional layers to deal with supervised learning tasks. In case of large graphs, to make the model more efficient in terms of running time and memory, we further relax the doubly stochastic matrices to row stochastic matrices. We empirically evaluate the model on graph classification and graph regression datasets and show that it achieves performance competitive with state-of-the-art models.


Node Feature Kernels Increase Graph Convolutional Network Robustness

arXiv.org Machine Learning

The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCN's performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.


Sparsifying the Update Step in Graph Neural Networks

arXiv.org Artificial Intelligence

Message-Passing Neural Networks (MPNNs), the most prominent Graph Neural Network (GNN) framework, celebrate much success in the analysis of graph-structured data. Concurrently, the sparsification of Neural Network models attracts a great amount of academic and industrial interest. In this paper, we conduct a structured study of the effect of sparsification on the trainable part of MPNNs known as the Update step. To this end, we design a series of models to successively sparsify the linear transform in the Update step. Specifically, we propose the ExpanderGNN model with a tuneable sparsification rate and the Activation-Only GNN, which has no linear transform in the Update step. In agreement with a growing trend in the literature, the sparsification paradigm is changed by initialising sparse neural network architectures rather than expensively sparsifying already trained architectures. Our novel benchmark models enable a better understanding of the influence of the Update step on model performance and outperform existing simplified benchmark models such as the Simple Graph Convolution. The ExpanderGNNs, and in some cases the Activation-Only models, achieve performance on par with their vanilla counterparts on several downstream tasks while containing significantly fewer trainable parameters. In experiments with matching parameter numbers, our benchmark models outperform the state-of-the-art GNN models. Our code is publicly available at: https://github.com/ChangminWu/ExpanderGNN.


Learning to Maximize Influence

arXiv.org Artificial Intelligence

As the field of machine learning for combinatorial optimization advances, traditional problems are resurfaced and readdressed through this new perspective. The overwhelming majority of the literature focuses on small graph problems, while several real-world problems are devoted to large graphs. Here, we focus on two such problems that are related: influence estimation, a \#P-hard counting problem, and influence maximization, an NP-hard problem. We develop GLIE, a Graph Neural Network (GNN) that inherently parameterizes an upper bound of influence estimation and train it on small simulated graphs. Experiments show that GLIE can provide accurate predictions faster than the alternatives for graphs 10 times larger than the train set. More importantly, it can be used on arbitrary large graphs for influence maximization, as the predictions can rank effectively seed sets even when the accuracy deteriorates. To showcase this, we propose a version of a standard Influence Maximization (IM) algorithm where we substitute traditional influence estimation with the predictions of GLIE.We also transfer GLIE into a reinforcement learning model that learns how to choose seeds to maximize influence sequentially using GLIE's hidden representations and predictions. The final results show that the proposed methods surpasses a previous GNN-RL approach and perform on par with a state-of-the-art IM algorithm.


Operation Embeddings for Neural Architecture Search

arXiv.org Artificial Intelligence

Neural Architecture Search (NAS) has recently gained increased attention, as a class of approaches that automatically searches in an input space of network architectures. A crucial part of the NAS pipeline is the encoding of the architecture that consists of the applied computational blocks, namely the operations and the links between them. Most of the existing approaches either fail to capture the structural properties of the architectures or use a hand-engineered vector to encode the operator information. In this paper, we propose the replacement of fixed operator encoding with learnable representations in the optimization process. This approach, which effectively captures the relations of different operations, leads to smoother and more accurate representations of the architectures and consequently to improved performance of the end task. Our extensive evaluation in ENAS benchmark demonstrates the effectiveness of the proposed operation embeddings to the generation of highly accurate models, achieving state-of-the-art performance. Finally, our method produces top-performing architectures that share similar operation and graph patterns, highlighting a strong correlation between architecture's structural properties and performance.


Learning Parametrised Graph Shift Operators

arXiv.org Machine Learning

In many domains data is currently represented as graphs and therefore, the graph representation of this data becomes increasingly important in machine learning. Network data is, implicitly or explicitly, always represented using a graph shift operator (GSO) with the most common choices being the adjacency, Laplacian matrices and their normalisations. In this paper, a novel parametrised GSO (PGSO) is proposed, where specific parameter values result in the most commonly used GSOs and message-passing operators in graph neural network (GNN) frameworks. The PGSO is suggested as a replacement of the standard GSOs that are used in state-of-the-art GNN architectures and the optimisation of the PGSO parameters is seamlessly included in the model training. It is proved that the PGSO has real eigenvalues and a set of real eigenvectors independent of the parameter values and spectral bounds on the PGSO are derived. PGSO parameters are shown to adapt to the sparsity of the graph structure in a study on stochastic blockmodel networks, where they are found to automatically replicate the GSO regularisation found in the literature. On several real-world datasets the accuracy of state-of-theart GNN architectures is improved by the inclusion of the PGSO in both nodeand graph-classification tasks. Graph representation learning has attracted a significant research interest over the last years, mainly due to the structural complexity of real-world data and applications (Hamilton et al., 2017b; Wu et al., 2020). The topology of the observations plays a central role when performing machine learning tasks on graph structured data.


United We Stand: Transfer Graph Neural Networks for Pandemic Forecasting

arXiv.org Machine Learning

The recent outbreak of COVID-19 has affected millions of individuals around the world and has posed a significant challenge to global healthcare. From the early days of the pandemic, it became clear that it is highly contagious and that human mobility contributes significantly to its spread. In this paper, we study the impact of population movement on the spread of COVID-19, and we capitalize on recent advances in the field of representation learning on graphs to capture the underlying dynamics. Specifically, we create a graph where nodes correspond to a country's regions and the edge weights denote human mobility from one region to another. Then, we employ graph neural networks to predict the number of future cases, encoding the underlying diffusion patterns that govern the spread into our learning model. Furthermore, to account for the limited amount of training data, we capitalize on the pandemic's asynchronous outbreaks across countries and use a model-agnostic meta-learning based method to transfer knowledge from one country's model to another's. We compare the proposed approach against simple baselines and more traditional forecasting techniques in 3 European countries. Experimental results demonstrate the superiority of our method, highlighting the usefulness of GNNs in epidemiological prediction. Transfer learning provides the best model, highlighting its potential to improve the accuracy of the predictions in case of secondary waves, if data from past/parallel outbreaks is utilized.


Predicting conversions in display advertising based on URL embeddings

arXiv.org Artificial Intelligence

Online display advertising is growing rapidly in recent years thanks to the automation of the ad buying process. Real-time bidding (RTB) allows the automated trading of ad impressions between advertisers and publishers through real-time auctions. In order to increase the effectiveness of their campaigns, advertisers should deliver ads to the users who are highly likely to be converted (i.e., purchase, registration, website visit, etc.) in the near future. In this study, we introduce and examine different models for estimating the probability of a user converting, given their history of visited URLs. Inspired by natural language processing, we introduce three URL embedding models to compute semantically meaningful URL representations. To demonstrate the effectiveness of the different proposed representation and conversion prediction models, we have conducted experiments on real logged events collected from an advertising platform.