Graph neural networks (GNNs) are increasingly used in critical human applications for predicting node labels in attributed graphs. Their ability to aggregate features from nodes' neighbors for accurate classification also has the capacity to exacerbate existing biases in data or to introduce new ones towards members from protected demographic groups. Thus, it is imperative to quantify how GNNs may be biased and to what extent their harmful effects may be mitigated. To this end, we propose two new GNN-agnostic interventions namely, (i) PFR-AX which decreases the separability between nodes in protected and non-protected groups, and (ii) PostProcess which updates model predictions based on a blackbox policy to minimize differences between error rates across demographic groups. Through a large set of experiments on four datasets, we frame the efficacies of our approaches (and three variants) in terms of their algorithmic fairness-accuracy tradeoff and bench- mark our results against three strong baseline interventions on three state-of-the-art GNN models. Our results show that no single intervention offers a universally optimal tradeoff, but PFR-AX and PostProcess provide granular control and improve model confidence when correctly predicting positive outcomes for nodes in protected groups.

Normalized-cut graph partitioning aims to divide the set of nodes in a graph into k disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the partitioning problem wherein nodes are characterized by a categorical sensitive attribute (e.g., gender or race) indicating membership to different demographic groups. Our goal is to ensure that each group is approximately proportionally represented in each cluster while minimizing the normalized cut value. To resolve this problem, we propose a two-phase spectral algorithm called FNM. In the first phase, we add an augmented Lagrangian term based on our fairness criteria to the objective function for obtaining a fairer spectral node embedding. Then, in the second phase, we design a rounding scheme to produce k clusters from the fair embedding that effectively trades off fairness and partition quality. Through comprehensive experiments on nine benchmark datasets, we demonstrate the superior performance of FNM compared with three baseline methods.

Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is minimized. Such summaries have immense applications in large-scale graph analytics due to their small size and high query processing efficiency. In this paper, we reformulate the loss minimization problem for summarization into an equivalent integer maximization problem. By initially allowing relaxed (fractional) solutions for integer maximization, we analytically expose the underlying connections to the spectral properties of the adjacency matrix. Consequently, we design an algorithm called SpecSumm that consists of two phases. In the first phase, motivated by spectral graph theory, we apply k-means clustering on the k largest (in magnitude) eigenvectors of the adjacency matrix to assign nodes to supernodes. In the second phase, we propose a greedy heuristic that updates the initial assignment to further improve summary quality. Finally, via extensive experiments on 11 datasets, we show that SpecSumm efficiently produces high-quality summaries compared to state-of-the-art summarization algorithms and scales to graphs with millions of nodes.

Linear classifiers are well-known to be vulnerable to adversarial attacks: they may predict incorrect labels for input data that are adversarially modified with small perturbations. However, this phenomenon has not been properly understood in the context of sketch-based linear classifiers, typically used in memory-constrained paradigms, which rely on random projections of the features for model compression. In this paper, we propose novel Fast-Gradient-Sign Method (FGSM) attacks for sketched classifiers in full, partial, and black-box information settings with regards to their internal parameters. We perform extensive experiments on the MNIST dataset to characterize their robustness as a function of perturbation budget. Our results suggest that, in the full-information setting, these classifiers are less accurate on unaltered input than their uncompressed counterparts but just as susceptible to adversarial attacks. But in more realistic partial and black-box information settings, sketching improves robustness while having lower memory footprint.

Distance oracles answer shortest-path queries between any pair of nodes in a graph. They are often built using succinct graph representations such as spanners, sketches, and compressors to minimize oracle size and query answering latency. Node embeddings, in particular, offer graph representations that place adjacent nodes nearby each other in a low-rank space. However, their use in the design of distance oracles has not been sufficiently studied. In this paper, we empirically compare exact distance oracles constructed based on a variety of node embeddings and other succinct representations. We evaluate twelve such oracles along three measures of efficiency: construction time, memory requirements, and query-processing time over fourteen real datasets and four synthetic graphs. We show that distances between embedding vectors are excellent estimators of graph distances when graphs are well-structured, but less so for more unstructured graphs. Overall, our findings suggest that exact oracles based on embeddings can be constructed faster than multi-dimensional scaling (MDS) but slower than compressed adjacency indexes, require less memory than landmark oracles but more than sparsifiers or indexes, can answer queries faster than indexes but slower than MDS, and are exact more often with a smaller additive error than spanners (that have multiplicative error) while not being lossless like adjacency lists. Finally, while the exactness of such oracles is infeasible to maintain for huge graphs even under large amounts of resources, we empirically demonstrate that approximate oracles based on GOSH embeddings can efficiently scale to graphs of 100M+ nodes with only small additive errors in distance estimations.

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O(min{d,N}log 1/ɛ) exam-ples, where d is the ambient dimension of the problem, N is the number of learners, and ɛ is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners’ internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners’ workload and the teacher’s cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives.

Stack Overflow, a Q&A site on programming, awards reputation points and badges (game elements) to users on performing various actions. Situating our work in Digital Signaling Theory, we investigate the role of these game elements in characterizing social qualities (specifically, popularity and impact) of its users. We operationalize these attributes using common metrics and apply statistical modeling to empirically quantify and validate the strength of these signals. Our results are based on a rich dataset of 3,831,147 users and their activities spanning nearly a decade since the site's inception in 2008. We present evidence that certain non-trivial badges, reputation scores and age of the user on the site positively correlate with popularity and impact. Further, we find that the presence of costly to earn and hard to observe signals qualitatively differentiates highly impactful users from highly popular users.