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Large infrastructure networks (e.g. for transportation and power distribution) require constant monitoring for failures, congestion, and other adversarial events. However, assigning a sensor to every link in the network is often infeasible due to placement and maintenance costs. Instead, sensors can be placed only on a few key links, and machine learning algorithms can be leveraged for the inference of missing measurements (e.g. traffic counts, power flows) across the network. This paper investigates the sensor placement problem for networks. We first formalize the problem under a flow conservation assumption and show that it is NP-hard to place a fixed set of sensors optimally. Next, we propose an efficient and adaptive greedy heuristic for sensor placement that scales to large networks. Our experiments, using datasets from real-world application domains, show that the proposed approach enables more accurate inference than existing alternatives from the literature. We demonstrate that considering even imperfect or incomplete ground-truth estimates can vastly improve the prediction error, especially when a small number of sensors is available., Comment: 9 pages, 6 figures

This paper addresses the problem of learning fair Graph Neural Networks (GNNs) under missing protected attributes. GNNs have achieved state-of-the-art results in many relevant tasks where decisions might disproportionately impact specific communities. However, existing work on fair GNNs assumes that either protected attributes are fully-observed or that the missing data imputation is fair. In practice, biases in the imputation will be propagated to the model outcomes, leading them to overestimate the fairness of their predictions. We address this challenge by proposing Better Fair than Sorry (BFtS), a fair missing data imputation model for protected attributes used by fair GNNs. The key design principle behind BFtS is that imputations should approximate the worst-case scenario for the fair GNN -- i.e. when optimizing fairness is the hardest. We implement this idea using a 3-player adversarial scheme where two adversaries collaborate against the fair GNN. Experiments using synthetic and real datasets show that BFtS often achieves a better fairness $\times$ accuracy trade-off than existing alternatives.

Explaining the decisions made by machine learning models for high-stakes applications is critical for increasing transparency and guiding improvements to these decisions. This is particularly true in the case of models for graphs, where decisions often depend on complex patterns combining rich structural and attribute data. While recent work has focused on designing so-called post-hoc explainers, the question of what constitutes a good explanation remains open. One intuitive property is that explanations should be sufficiently informative to enable humans to approximately reproduce the predictions given the data. However, we show that post-hoc explanations do not achieve this goal as their explanations are highly dependent on fixed model parameters (e.g., learned GNN weights). To address this challenge, this paper proposes RAGE (Robust Ante-hoc Graph Explainer), a novel and flexible ante-hoc explainer designed to discover explanations for a broad class of graph neural networks using bilevel optimization. RAGE is able to efficiently identify explanations that contain the full information needed for prediction while still enabling humans to rank these explanations based on their influence. Our experiments, based on graph classification and regression, show that RAGE explanations are more robust than existing post-hoc and ante-hoc approaches and often achieve similar or better accuracy than state-of-the-art models.

Link prediction, which consists of predicting edges based on graph features, is a fundamental task in many graph applications. As for several related problems, Graph Neural Networks (GNNs), which are based on an attribute-centric message-passing paradigm, have become the predominant framework for link prediction. GNNs have consistently outperformed traditional topology-based heuristics, but what contributes to their performance? Are there simpler approaches that achieve comparable or better results? To answer these questions, we first identify important limitations in how GNN-based link prediction methods handle the intrinsic class imbalance of the problem -- due to the graph sparsity -- in their training and evaluation. Moreover, we propose Gelato, a novel topology-centric framework that applies a topological heuristic to a graph enhanced by attribute information via graph learning. Our model is trained end-to-end with an N-pair loss on an unbiased training set to address class imbalance. Experiments show that Gelato is 145% more accurate, trains 11 times faster, infers 6,000 times faster, and has less than half of the trainable parameters compared to state-of-the-art GNNs for link prediction., Comment: 15 pages

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify opportunities to advance the state-of-the-art. Meanwhile, existing work has left several fundamental questions -- such as how embeddings capture different structural scales and how they should be applied for effective link prediction -- unanswered. This paper addresses these challenges with an analytical framework for random-walk based graph embedding that consists of three components: a random-walk process, a similarity function, and an embedding algorithm. Our framework not only categorizes many existing approaches but naturally motivates new ones. With it, we illustrate novel ways to incorporate embeddings at multiple scales to improve downstream task performance. We also show that embeddings based on autocovariance similarity, when paired with dot product ranking for link prediction, outperform state-of-the-art methods based on Pointwise Mutual Information similarity by up to 100%., Comment: Accepted to KDD 2021

Event detection is a critical task for timely decision-making in graph analytics applications. Despite the recent progress towards deep learning on graphs, event detection on dynamic graphs presents particular challenges to existing architectures. Real-life events are often associated with sudden deviations of the normal behavior of the graph. However, existing approaches for dynamic node embedding are unable to capture the graph-level dynamics related to events. In this paper, we propose DyGED, a simple yet novel deep learning model for event detection on dynamic graphs. DyGED learns correlations between the graph macro dynamics -- i.e. a sequence of graph-level representations -- and labeled events. Moreover, our approach combines structural and temporal self-attention mechanisms to account for application-specific node and time importances effectively. Our experimental evaluation, using a representative set of datasets, demonstrates that DyGED outperforms competing solutions in terms of event detection accuracy by up to 8.5% while being more scalable than the top alternatives. We also present case studies illustrating key features of our model., Comment: Longer version of "Graph Macro Dynamics with Self-Attention for Event Detection" accepted to DLG-AAAI 2023

From the 2016 U.S. presidential election to the 2021 Capitol riots to the spread of misinformation related to COVID-19, many have blamed social media for today's deeply divided society. Recent advances in machine learning for signed networks hold the promise to guide small interventions with the goal of reducing polarization in social media. However, existing models are especially ineffective in predicting conflicts (or negative links) among users. This is due to a strong correlation between link signs and the network structure, where negative links between polarized communities are too sparse to be predicted even by state-of-the-art approaches. To address this problem, we first design a partition-agnostic polarization measure for signed graphs based on the signed random-walk and show that many real-world graphs are highly polarized. Then, we propose POLE (POLarized Embedding for signed networks), a signed embedding method for polarized graphs that captures both topological and signed similarities jointly via signed autocovariance. Through extensive experiments, we show that POLE significantly outperforms state-of-the-art methods in signed link prediction, particularly for negative links with gains of up to one order of magnitude., Comment: Accepted to WSDM 2022

Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group fairness in the $k$-clustering problem, fairness at an individual level is relatively less explored. We introduce a new notion of individual fairness in $k$-clustering based on features not necessarily used for clustering. We show that this problem is NP-hard and does not admit a constant factor approximation. Therefore, we design a randomized algorithm that guarantees approximation both in terms of minimizing the clustering distance objective and individual fairness under natural restrictions on the distance metric and fairness constraints. Finally, our experimental results against six competing baselines validate that our algorithm produces individually fairer clusters than the fairest baseline by 12.5% on average while also being less costly in terms of the clustering objective than the best baseline by 34.5% on average.

Network robustness is a measure a network's ability to survive adversarial attacks. But not all parts of a network are equal. K-cores, which are dense subgraphs, are known to capture some of the key properties of many real-life networks. Therefore, previous work has attempted to model network robustness via the stability of its k-core. However, these approaches account for a single core value and thus fail to encode a global network resilience measure. In this paper, we address this limitation by proposing a novel notion of network resilience that is defined over all cores. In particular, we evaluate the stability of the network under node removals with respect to each node's initial core. Our goal is to compute robustness via a combinatorial problem: find b most critical nodes to delete such that the number of nodes that fall from their initial cores is maximized. One of our contributions is showing that it is NP-hard to achieve any polynomial factor approximation of the given objective. We also present a fine-grained complexity analysis of this problem under the lens of parameterized complexity theory for several natural parameters. Moreover, we show two applications of our notion of robustness: measuring the evolution of species and characterizing networks arising from different domains., Comment: Accepted as a full paper in AAMAS'21

Recently, online social networks have become major battlegrounds for political campaigns, viral marketing, and the dissemination of news. As a consequence, ''bad actors'' are increasingly exploiting these platforms, becoming a key challenge for their administrators, businesses and the society in general. The spread of fake news is a classical example of the abuse of social networks by these actors. While some have advocated for stricter policies to control the spread of misinformation in social networks, this often happens in detriment of their democratic and organic structure. In this paper we study how to limit the influence of a target set of users in a network via the removal of a few edges. The idea is to control the diffusion processes while minimizing the amount of disturbance in the network structure. We formulate the influence limitation problem in a data-driven fashion, by taking into account past propagation traces. Moreover, we consider two types of constraints over the set of edge removals, a budget constraint and also a, more general, set of matroid constraints. These problems lead to interesting challenges in terms of algorithm design. For instance, we are able to show that influence limitation is APX-hard and propose deterministic and probabilistic approximation algorithms for the budgeted and matroid version of the problem, respectively. Our experiments show that the proposed solutions outperform the baselines by up to 40%.

K-cores are maximal induced subgraphs where all vertices have degree at least k. These dense patterns have applications in community detection, network visualization and protein function prediction. However, k-cores can be quite unstable to network modifications, which motivates the question: How resilient is the k-core structure of a network, such as the Web or Facebook, to edge deletions? We investigate this question from an algorithmic perspective. More specifically, we study the problem of computing a small set of edges for which the removal minimizes the $k$-core structure of a network. This paper provides a comprehensive characterization of the hardness of the k-core minimization problem (KCM), including innaproximability and fixed-parameter intractability. Motivated by such a challenge in terms of algorithm design, we propose a novel algorithm inspired by Shapley value -- a cooperative game-theoretic concept -- that is able to leverage the strong interdependencies in the effects of edge removals in the search space. As computing Shapley values is also NP-hard, we efficiently approximate them using a randomized algorithm with probabilistic guarantees. Our experiments, using several real datasets, show that the proposed algorithm outperforms competing solutions in terms of k-core minimization while being able to handle large graphs. Moreover, we illustrate how KCM can be applied in the analysis of the k-core resilience of networks., Comment: To appear as an extended abstract in AAMAS 2020 and as a full paper in IJCAI 2020

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold in many modern applications where graphs are highly dynamic. In this paper, we introduce the sparsest and normalized cut problems in temporal graphs, which generalize their standard definitions by enforcing the smoothness of cuts over time. We propose novel formulations and algorithms for computing temporal cuts using spectral graph theory, multiplex graphs, divide-and-conquer and low-rank matrix approximation. Furthermore, we extend our formulation to dynamic graph signals, where cuts also capture node values, as graph wavelets. Experiments show that our solutions are accurate and scalable, enabling the discovery of dynamic communities and the analysis of dynamic graph processes.

Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors.In hyperlinked environments, such as the Web, where users navigate via clicks, central content receives high traffic, becoming targets for advertising campaigns. While there is an extensive amount of work on centrality measures and their efficient computation, controlling nodes' centrality via network updates is a more recent and challenging problem. Performing minimal modifications to a network to achieve a desired property falls under the umbrella of network design problems. This paper is focused on improving the coverage centrality of a set of nodes, which is the number of pairs of nodes that have a shortest path passing through the set, by adding edges to the network. We prove strong inapproximability results and propose a greedy algorithm for maximizing coverage centrality. To ensure scalability to large networks, we also design an efficient sampling algorithm for the problem. In addition to providing an extensive empirical evaluation of our algorithms, we also show that, under some realistic constraints, the proposed solutions achieve almost-optimal approximation for coverage centrality maximization.

Detecting a small number of outliers from a set of data observations is always challenging. This problem is more difficult in the setting of multiple network samples, where computing the anomalous degree of a network sample is generally not sufficient. In fact, explaining why the network is exceptional, expressed in the form of subnetwork, is also equally important. In this paper, we develop a novel algorithm to address these two key problems. We treat each network sample as a potential outlier and identify subnetworks that mostly discriminate it from nearby regular samples. The algorithm is developed in the framework of network regression combined with the constraints on both network topology and L1-norm shrinkage to perform subnetwork discovery. Our method thus goes beyond subspace/subgraph discovery and we show that it converges to a global optimum. Evaluation on various real-world network datasets demonstrates that our algorithm not only outperforms baselines in both network and high dimensional setting, but also discovers highly relevant and interpretable local subnetworks, further enhancing our understanding of anomalous networks.

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can exploit the intrinsic smoothness of these datasets in order to represent them in a both compact and accurate manner. However, how to discover wavelet bases that capture the geometry of the data with respect to the signal as well as the graph structure remains an open question. In this paper, we study the problem of computing graph wavelet bases via sparse cuts in order to produce low-dimensional encodings of data-driven bases. This problem is connected to known hard problems in graph theory (e.g. multiway cuts) and thus requires an efficient heuristic. We formulate the basis discovery task as a relaxation of a vector optimization problem, which leads to an elegant solution as a regularized eigenvalue computation. Moreover, we propose several strategies in order to scale our algorithm to large graphs. Experimental results show that the proposed algorithm can effectively encode both the graph structure and signal, producing compressed and accurate representations for vertex values in a wide range of datasets (e.g. sensor and gene networks) and significantly outperforming the best baseline.

Recent spatio-temporal data applications, such as car-shar\-ing and smart cities, impose new challenges regarding the scalability and timeliness of data processing systems. Trajectory compression is a promising approach for scaling up spatio-temporal databases. However, existing techniques fail to address the online setting, in which a compressed version of a trajectory stream has to be maintained over time. In this paper, we introduce ONTRAC, a new framework for map-matched online trajectory compression. ONTRAC learns prediction models for suppressing updates to a trajectory database using training data. Two prediction schemes are proposed, one for road segments via a Markov model and another for travel-times by combining Quadratic Programming and Expectation Maximization. Experiments show that ONTRAC outperforms the state-of-the-art offline technique even when long update delays (4 mininutes) are allowed and achieves up to 21 times higher compression ratio for travel-times. Moreover, our approach increases database scalability by up to one order of magnitude.

In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph induced by a particular attribute set. Existing methods are not able to extract relevant knowledge regarding how vertex attributes interact with dense subgraphs. Structural correlation pattern mining combines aspects of frequent itemset and quasi-clique mining problems. We propose statistical significance measures that compare the structural correlation of attribute sets against their expected values using null models. Moreover, we evaluate the interestingness of structural correlation patterns in terms of size and density. An efficient algorithm that combines search and pruning strategies in the identification of the most relevant structural correlation patterns is presented. We apply our method for the analysis of three real-world attributed graphs: a collaboration, a music, and a citation network, verifying that it provides valuable knowledge in a feasible time., Comment: VLDB2012