Silvia Beddar-Wiesing

Silvia Beddar-Wiesing, Giuseppe Alessio D'Inverno, Caterina Graziani et al.

Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence.

Josephine M. Thomas, Alice Moallemy-Oureh, Silvia Beddar-Wiesing et al.

Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the represented problem. To address cutting-edge problems based on graph data, the research field of Graph Neural Networks (GNNs) has emerged. Despite the field's youth and the speed at which new models are developed, many recent surveys have been published to keep track of them. Nevertheless, it has not yet been gathered which GNN can process what kind of graph types. In this survey, we give a detailed overview of already existing GNNs and, unlike previous surveys, categorize them according to their ability to handle different graph types and properties. We consider GNNs operating on static and dynamic graphs of different structural constitutions, with or without node or edge attributes. Moreover, we distinguish between GNN models for discrete-time or continuous-time dynamic graphs and group the models according to their architecture. We find that there are still graph types that are not or only rarely covered by existing GNN models. We point out where models are missing and give potential reasons for their absence.

Alice Moallemy-Oureh, Silvia Beddar-Wiesing, Yannick Nagel et al.

Temporal Point Processes (TPPs) have recently become increasingly interesting for learning dynamics in graph data. A reason for this is that learning on dynamic graph data is becoming more relevant, since data from many scientific fields, ranging from mathematics, biology, social sciences, and physics to computer science, is naturally related and inherently dynamic. In addition, TPPs provide a meaningful characterization of event streams and a prediction mechanism for future events. Therefore, (semi-)parameterized Neural TPPs have been introduced whose characterization can be (partially) learned and, thus, enable the representation of more complex phenomena. However, the research on modeling dynamic graphs with TPPs is relatively young, and only a few models for node attribute changes or evolving edges have been proposed yet. To allow for learning on fully dynamic graph streams, i.e., graphs that can change in their structure (addition/deletion of nodes/edge) and in their node/edge attributes, we propose a Marked Neural Spatio-Temporal Point Process (MNSTPP). It leverages a Dynamic Graph Neural Network to learn a Marked TPP that handles attributes and spatial data to model and predict any event in a graph stream.

Silvia Beddar-Wiesing, Alice Moallemy-Oureh, Marie Kempkes et al.

Machine Learning is a diverse field applied across various domains such as computer science, social sciences, medicine, chemistry, and finance. This diversity results in varied evaluation approaches, making it difficult to compare models effectively. Absolute evaluation measures offer a practical solution by assessing a model's performance on a fixed scale, independent of reference models and data ranges, enabling explicit comparisons. However, many commonly used measures are not universally applicable, leading to a lack of comprehensive guidance on their appropriate use. This survey addresses this gap by providing an overview of absolute evaluation metrics in ML, organized by the type of learning problem. While classification metrics have been extensively studied, this work also covers clustering, regression, and ranking metrics. By grouping these measures according to the specific ML challenges they address, this survey aims to equip practitioners with the tools necessary to select appropriate metrics for their models. The provided overview thus improves individual model evaluation and facilitates meaningful comparisons across different models and applications.

Silvia Beddar-Wiesing, Alice Moallemy-Oureh

Graph Neural Networks (GNNs) are known to match the distinguishing power of the 1-Weisfeiler-Lehman (1-WL) test, and the resulting partitions coincide with the unfolding tree equivalence classes of graphs. Preserving this equivalence, GNNs can universally approximate any target function on graphs in probability up to any precision. However, these results are limited to attributed discrete-dynamic graphs represented as sequences of connected graph snapshots. Real-world systems, such as communication networks, financial transaction networks, and molecular interactions, evolve asynchronously and may split into disconnected components. In this paper, we extend the theory of attributed discrete-dynamic graphs to attributed continuous-time dynamic graphs with arbitrary connectivity. To this end, we introduce a continuous-time dynamic 1-WL test, prove its equivalence to continuous-time dynamic unfolding trees, and identify a class of continuous-time dynamic GNNs (CGNNs) based on discrete-dynamic GNN architectures that retain both distinguishing power and universal approximation guarantees. Our constructive proofs further yield practical design guidelines, emphasizing a compact and expressive CGNN architecture with piece-wise continuously differentiable temporal functions to process asynchronous, disconnected graphs.

Silvia Beddar-Wiesing, Maarten Bieshaar

Fusion is a common tool for the analysis and utilization of available datasets and so an essential part of data mining and machine learning processes. However, a clear definition of the type of fusion is not always provided due to inconsistent literature. In the following, the process of fusion is defined depending on the fusion components and the abstraction level on which the fusion occurs. The focus in the first part of the paper at hand is on the clear definition of the terminology and the development of an appropriate ontology of the fusion components and the fusion level. In the second part, common fusion techniques are presented.