We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Social physics

Η τάση για ολοένα αυξανόμeνη ποικιλία προϊόντων eπηρeάζeι σημαντικά το σχeδιασμό και τη λeιτουργία των συστημάτων παραγωγής. Το eυρέως διαδeδομένο πρότυπο της μαζική eξατομίκeυσης προϊόντων προσφέρeι λύσeις σe αυτές τις ανάγκeς. Ωστόσο, η έλλeιψη κατάλληλων eργαλeίων για την υποστήριξη πραγματικών βιομηχανικών eφαρμογών της μαζικής eξατομίκeυσης eίναι eμφανής. Μια τέτοια eφαρμογή eίναι ο σχeδιασμός δικτύων παραγωγής και ο eπανασχeδιασμός τους ώστe να προσαρμοστούν σe διαφορeτικά προφίλ ζήτησης προϊόντων. Η eπίλυση τέτοιων προβλημάτων eίναι αδύνατον να eπιτeυχθeί αποδοτικά μe βάση μόνο την eμπeιρία των ομάδων σχeδιασμού και προγραμματισμού δικτύων. Νέοι τρόποι για τον eντοπισμό αποδοτικών δικτύων παραγωγής σe γρήγορο χρόνο eίναι απαραίτητοι ώστe να eπιτeυχθeί η μeίωση στους χρόνους παράδοσης. 
Μe σκοπό την υποστήριξη αποφάσeων σχeδιασμού και λeιτουργίας δικτύων παραγωγής μέσω, η διατριβή αυτή προτeίνeι μια έξυπνη πολύ-κριτηριακή διαδικασία λήψης αποφάσeων που βασίζeται σe τeχνολογίeς προσομοίωσης. Μe βάση τη μέθοδο αυτή, αναπτύσσeται η πλατφόρμα λογισμικού “Design and Planning of Manufacturing Networks” - DPMN© που αποτeλeίται από τα:
- “User Adaptive Design System (UADS)” που eπιτρέπeι στον πeλάτη να eξατομικeύσeι (υπό πeριορισμούς) ένα προϊόν online
- “Decentralised Manufacturing Platform (DEMAP)” που eπιτρέπeι τη δημιουργία, αξιολόγηση, και eπιλογή eναλλακτικών δικτύων παραγωγής και μeταφοράς eξατομικeυμένων προϊόντων
Η μέθοδος και η πλατφόρμα λογισμικού eπικeντρώνονται στην υποστήριξη eταιριών που προσφέρουν eξατομικeυμένα προϊόντα/υπηρeσίeς μe δύο τρόπους: 1) υποστηρίζοντας την eνσωμάτωση των πeλατών στον σχeδιασμό προϊόντων και 2) eπιτρέποντας στους κατασκeυαστές να σχeδιάσουν / eπανασχeδιάσουν αποδοτικά αποκeντρωμένα δίκτυα παραγωγής. 
Η διαδικασία λήψης αποφάσeων υποστηρίζeται από έναν Έξυπνο Αλγόριθμο Αναζήτησης, ο οποίος δημιουργeί και αξιολογeί eναλλακτικούς σχeδιασμούς δικτύων eνάντια σe πολλαπλά κριτήρια όπως: κόστος και χρόνος παραγωγής και μeταφορών, eυeλιξία, ποιότητα, αξιοπιστία, δυναμική πολυπλοκότητα, eτήσιο όγκο παραγωγής, και πeριβαλλοντικό αντίκτυπο. Η απόδοση του αλγόριθμου διeρeυνάται μέσω στατιστικής ανάλυσης και σχeδιασμού πeιραμάτων. Eπίσης, μέσω προσομοίωσης διακριτών γeγονότων, διeρeυνάται ο αντίκτυπος που έχουν τα μeταβαλλόμeνα προφίλ ζήτησης προϊόντων στη λeιτουργία των δικτύων παραγωγής. 
Τέλος, διeρeυνάται η πρακτική eφαρμογή της μeθόδου και της πλατφόρμας σe δυο πιλοτικά σeνάρια πού αναπτύχθηκαν σe συνeργασία μe δυο Eυρωπαϊκές eταιρίeς: έναν κατασκeυαστή αυτοκίνητων και μια eταιρία κατασκeυής eργαλeιομηχανών CNC.

Development of methods and tools for the design and operation of manufacturing networks for mass customisation

Deep learning methods are achieving ever-increasing performance on many artificial intelligence tasks. A major limitation of deep models is that they are not amenable to interpretability. This limitation can be circumvented by developing post hoc techniques to explain the predictions, giving rise to the area of explainability. Recently, explainability of deep models on images and texts has achieved significant progress. In the area of graph data, graph neural networks (GNNs) and their explainability are experiencing rapid developments. However, there is neither a unified treatment of GNN explainability methods, nor a standard benchmark and testbed for evaluations. In this survey, we provide a unified and taxonomic view of current GNN explainability methods. Our unified and taxonomic treatments of this subject shed lights on the commonalities and differences of existing methods and set the stage for further methodological developments. To facilitate evaluations, we generate a set of benchmark graph datasets specifically for GNN explainability. We summarize current datasets and metrics for evaluating GNN explainability. Altogether, this work provides a unified methodological treatment of GNN explainability and a standardized testbed for evaluations.

Explainability in Graph Neural Networks: A Taxonomic Survey.

Summarized by the efficient market hypothesis, the idea that stock prices fully reflect all available information is always confronted with the behavior of real-world markets. While there is plenty of evidence indicating and quantifying the efficiency of stock markets, most studies assume this efficiency to be constant over time so that its dynamical and collective aspects remain poorly understood. Here we define the time-varying efficiency of stock markets by calculating the permutation entropy within sliding time-windows of log-returns of stock market indices. We show that major world stock markets can be hierarchically classified into several groups that display similar long-term efficiency profiles. However, we also show that efficiency ranks and clusters of markets with similar trends are only stable for a few months at a time. We thus propose a network representation of stock markets that aggregates their short-term efficiency patterns into a global and coherent picture. We find this financial network to be strongly entangled while also having a modular structure that consists of two distinct groups of stock markets. Our results suggest that stock market efficiency is a collective phenomenon that can drive its operation at a high level of informational efficiency, but also places the entire system under risk of failure.

/pdf/collective-dynamics-of-stock-market-efficiency-2gxjdzk3j2.pdf

Collective dynamics of stock market efficiency

Finding communities in complex networks is a challenging task and one promising approach is the Stochastic Block Model (SBM). But the influences from various fields led to a diversity of variants and inference methods. Therefore, a comparison of the existing techniques and an independent analysis of their capabilities and weaknesses is needed. As a first step, we review the development of different SBM variants such as the degree-corrected SBM of Karrer and Newman or Peixoto’s hierarchical SBM. Beside stating all these variants in a uniform notation, we show the reasons for their development. Knowing the variants, we discuss a variety of approaches to infer the optimal partition like the Metropolis-Hastings algorithm. We perform our analysis based on our extension of the Girvan-Newman test and the Lancichinetti-Fortunato-Radicchi benchmark as well as a selection of some real world networks. Using these results, we give some guidance to the challenging task of selecting an inference method and SBM variant. In addition, we give a simple heuristic to determine the number of steps for the Metropolis-Hastings algorithms that lack a usual stop criterion. With our comparison, we hope to guide researches in the field of SBM and highlight the problem of existing techniques to focus future research. Finally, by making our code freely available, we want to promote a faster development, integration and exchange of new ideas.

/pdf/stochastic-block-models-a-comparison-of-variants-and-4xuq3iapwc.pdf

Stochastic block models: A comparison of variants and inference methods.

Complex networks of material flow in manufacturing and logistics: Modeling, analysis, and prediction using stochastic block models

With the ever-increasing popularity and applications of graph neural networks, several proposals have been made to interpret and understand the decisions of a GNN model. Explanations for a GNN model differ in principle from other input settings. It is important to attribute the decision to input features and other related instances connected by the graph structure. We find that the previous explanation generation approaches that maximize the mutual information between the label distribution produced by the GNN model and the explanation to be restrictive. Specifically, existing approaches do not enforce explanations to be predictive, sparse, or robust to input perturbations. 
In this paper, we lay down some of the fundamental principles that an explanation method for GNNs should follow and introduce a metric fidelity as a measure of the explanation's effectiveness. We propose a novel approach Zorro based on the principles from rate-distortion theory that uses a simple combinatorial procedure to optimize for fidelity. Extensive experiments on real and synthetic datasets reveal that Zorro produces sparser, stable, and more faithful explanations than existing GNN explanation approaches.

Zorro: Valid, Sparse, and Stable Explanations in Graph Neural Networks.

The problem of interpreting the decisions of machine learning is a well-researched and important. We are interested in a speciﬁc type of machine learning model that deals with graph data called graph neural networks. Evaluating interpretability approaches for graph neural networks (GNN) speciﬁcally are known to be challenging due to the lack of a commonly accepted benchmark. Given a GNN model, several interpretability approaches exist to explain GNN models with diverse (sometimes conﬂicting) evaluation methodologies. In this paper, we propose a benchmark for evaluating the explainability approaches for GNNs called B AGEL . In B AGEL , we ﬁrstly propose four diverse GNN explanation evaluation regimes – 1) faithfulness , 2) sparsity , 3) correctness , and 4) plausibility . We reconcile multiple evaluation metrics in the existing literature and cover diverse notions for a holistic evaluation. Our graph datasets range from citation networks, document graphs, to graphs from molecules and proteins. We conduct an extensive empirical study on four GNN models and nine post-hoc explanation approaches for node and graph classiﬁcation tasks. We open both the benchmarks and reference implementations and make them available at https://github.com/Mandeep-Rathee/Bagel-benchmark .

BAGEL: A Benchmark for Assessing Graph Neural Network Explanations

Privacy and interpretability are two important ingredients for achieving trustworthy machine learning. We study the interplay of these two aspects in graph machine learning through graph reconstruction attacks. The goal of the adversary here is to reconstruct the graph structure of the training data given access to model explanations. Based on the different kinds of auxiliary information available to the adversary, we propose several graph reconstruction attacks. We show that additional knowledge of post-hoc feature explanations substantially increases the success rate of these attacks. Further, we investigate in detail the differences between attack performance with respect to three different classes of explanation methods for graph neural networks: gradient-based, perturbation-based, and surrogate model-based methods. While gradient-based explanations reveal the most in terms of the graph structure, we find that these explanations do not always score high in utility. For the other two classes of explanations, privacy leakage increases with an increase in explanation utility. Finally, we propose a defense based on a randomized response mechanism for releasing the explanations, which substantially reduces the attack success rate. Our code is available at https://github.com/iyempissy/graph-stealing-attacks-with-explanation.

Thorben Funke

Papers

Stochastic block models: A comparison of variants and inference methods.

Complex networks of material flow in manufacturing and logistics: Modeling, analysis, and prediction using stochastic block models

Zorro: Valid, Sparse, and Stable Explanations in Graph Neural Networks.

BAGEL: A Benchmark for Assessing Graph Neural Network Explanations

Private Graph Extraction via Feature Explanations