Predicting the edge weights of a graph is a critical task across many domains. Some examples include predicting traffic flow in transportation networks, strength of interactions in protein-protein networks, and collaboration frequency in co-authorship networks. Graph Neural Networks have been very successful in edge-weight prediction tasks. However, these predictions lack rigorous statistical uncertainty quantification. Recent work has demonstrated the efficacy of conformal inference in quantifying the uncertainties of the predictions made by graph neural networks. However, there has been limited research in conformal inference for edge-weight prediction.

While graph neural networks (GNNs) are widely used for node and graph representation learning tasks, the reliability of GNN uncertainty estimates under distribution shifts remains relatively under-explored. Indeed, while post-hoc calibration strategies can be used to improve in-distribution calibration, they need not also improve calibration under distribution shift. However, techniques which produce GNNs with better intrinsic uncertainty estimates are particularly valuable, as they can always be combined with post-hoc strategies later. Therefore, in this work, we propose G-$\Delta$UQ, a novel training framework designed to improve intrinsic GNN uncertainty estimates. Our framework adapts the principle of stochastic data centering to graph data through novel graph anchoring strategies, and is able to support partially stochastic GNNs. While, the prevalent wisdom is that fully stochastic networks are necessary to obtain reliable estimates, we find that the functional diversity induced by our anchoring strategies when sampling hypotheses renders this unnecessary and allows us to support G-$\Delta$UQ on pretrained models. Indeed, through extensive evaluation under covariate, concept and graph size shifts, we show that G-$\Delta$UQ leads to better calibrated GNNs for node and graph classification. Further, it also improves performance on the uncertainty-based tasks of out-of-distribution detection and generalization gap estimation. Overall, our work provides insights into uncertainty estimation for GNNs, and demonstrates the utility of G-$\Delta$UQ in obtaining reliable estimates.

In many scientific endeavors, increasingly abstract representations of data allow for new interpretive methodologies and conceptualization of phenomena. For example, moving from raw imaged pixels to segmented and reconstructed objects allows researchers new insights and means to direct their studies toward relevant areas. Thus, the development of new and improved methods for segmentation remains an active area of research. With advances in machine learning and neural networks, scientists have been focused on employing deep neural networks such as U-Net to obtain pixel-level segmentations, namely, defining associations between pixels and corresponding/referent objects and gathering those objects afterward. Topological analysis, such as the use of the Morse-Smale complex to encode regions of uniform gradient flow behavior, offers an alternative approach: first, create geometric priors, and then apply machine learning to classify. This approach is empirically motivated since phenomena of interest often appear as subsets of topological priors in many applications. Using topological elements not only reduces the learning space but also introduces the ability to use learnable geometries and connectivity to aid the classification of the segmentation target. In this article, we describe an approach to creating learnable topological elements, explore the application of ML techniques to classification tasks in a number of areas, and demonstrate this approach as a viable alternative to pixel-level classification, with similar accuracy, improved execution time, and requiring marginal training data.

Topological analysis reveals meaningful structure in data from a variety of domains. Tasks such as image segmentation can be effectively performed on an image’s topological connectivity using graph neural networks (GNNs). We propose two methods for using GNNs to learn from the hierarchical information captured by complexes at multiple levels of topological persistence: one modifies the training procedure of an existing GNN, and one extends the message passing across all levels of the complex. Experiments on real-world data from three domains show the performance benefits to GNNs from using a hierarchical topological structure.

Model agnostic meta-learning algorithms aim to infer priors from several observed tasks that can then be used to adapt to a new task with few examples. Given the inherent diversity of tasks arising in existing benchmarks, recent methods have resorted to task-specific adaptation of the prior. Our goal is to improve generalization of meta learners when the task distribution contains challenging distribution shifts and semantic disparities. To this end, we introduce CAML (Contrastive Knowledge-Augmented Meta Learning), a knowledge-enhanced few-shot learning approach that evolves a knowledge graph to encode historical experience, and employs a contrastive distillation strategy to leverage the encoded knowledge for task-aware modulation of the base learner. In addition to the standard few-shot task adaptation, we also consider the more challenging multi-domain task adaptation and few-shot dataset generalization settings in our evaluation with standard benchmarks. Our empirical study shows that CAML (i) enables simple task encoding schemes; (ii) eliminates the need for knowledge extraction at inference time; and most importantly, (iii) effectively aggregates historical experience thus leading to improved performance in both multi-domain adaptation and dataset generalization.

Network alignment, or the task of finding corresponding nodes in different networks, is an important problem formulation in many application domains. We propose CAPER, a multilevel alignment framework that Coarsens the input graphs, Aligns the coarsened graphs, Projects the alignment solution to finer levels and Refines the alignment solution. We show that CAPER can improve upon many different existing network alignment algorithms by enforcing alignment consistency across multiple graph resolutions: nodes matched at finer levels should also be matched at coarser levels. CAPER also accelerates the use of slower network alignment methods, at the modest cost of linear-time coarsening and refinement steps, by allowing them to be run on smaller coarsened versions of the input graphs. Experiments show that CAPER can improve upon diverse network alignment methods by an average of 33% in accuracy and/or an order of magnitude faster in runtime.

Recent analyses of self-supervised learning (SSL) find the following data-centric properties to be critical for learning good representations: invariance to task-irrelevant semantics, separability of classes in some latent space, and recoverability of labels from augmented samples. However, given their discrete, non-Euclidean nature, graph datasets and graph SSL methods are unlikely to satisfy these properties. This raises the question: how do graph SSL methods, such as contrastive learning (CL), work well? To systematically probe this question, we perform a generalization analysis for CL when using generic graph augmentations (GGAs), with a focus on data-centric properties. Our analysis yields formal insights into the limitations of GGAs and the necessity of task-relevant augmentations. As we empirically show, GGAs do not induce task-relevant invariances on common benchmark datasets, leading to only marginal gains over naive, untrained baselines. Our theory motivates a synthetic data generation process that enables control over task-relevant information and boasts pre-defined optimal augmentations. This flexible benchmark helps us identify yet unrecognized limitations in advanced augmentation techniques (e.g., automated methods). Overall, our work rigorously contextualizes, both empirically and theoretically, the effects of data-centric properties on augmentation strategies and learning paradigms for graph SSL.

While most network embedding techniques model the proximity between nodes in a network, recently there has been significant interest in structural embeddings that are based on node equivalences , a notion rooted in sociology: equivalences or positions are collections of nodes that have similar roles—i.e., similar functions, ties or interactions with nodes in other positions—irrespective of their distance or reachability in the network. Unlike the proximity-based methods that are rigorously evaluated in the literature, the evaluation of structural embeddings is less mature. It relies on small synthetic or real networks with labels that are not perfectly defined, and its connection to sociological equivalences has hitherto been vague and tenuous. With new node embedding methods being developed at a breakneck pace, proper evaluation, and systematic characterization of existing approaches will be essential to progress. To fill in this gap, we set out to understand what types of equivalences structural embeddings capture. We are the first to contribute rigorous intrinsic and extrinsic evaluation methodology for structural embeddings, along with carefully-designed, diverse datasets of varying sizes. We observe a number of different evaluation variables that can lead to different results (e.g., choice of similarity measure, classifier, and label definitions). We find that degree distributions within nodes’ local neighborhoods can lead to simple yet effective baselines in their own right and guide the future development of structural embedding. We hope that our findings can influence the design of further node embedding methods and also pave the way for more comprehensive and fair evaluation of structural embedding methods.

Network alignment, or the task of finding meaningful node correspondences between nodes in di↵erent graphs, is an important graph mining task with many scientific and industrial applications.An important principle for network alignment is matched neighborhood consistency (MNC): nodes that are close in one graph should be matched to nodes that are close in the other graph.We theoretically demonstrate a close relationship between MNC and alignment accuracy.As many existing network alignment methods struggle to preserve topological consistency in di cult scenarios, we show how to refine their solutions by improving their MNC.Our refinement method, RefiNA, is straightforward to implement, admits scalable sparse approximation, and can be paired post hoc with any network alignment method.Extensive experiments show that RefiNA increases the accuracy of diverse unsupervised network alignment methods by up to 90%, making them robust enough to align graphs that are 5⇥ more topologically di↵erent than were considered in prior work.

While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.

Network alignment, the process of finding correspondences between nodes in different graphs, has many scientific and industrial applications. Existing unsupervised network alignment methods find suboptimal alignments that break up node neighborhoods, i.e. do not preserve matched neighborhood consistency. To improve this, we propose CONE-Align, which models intra-network proximity with node embeddings and uses them to match nodes across networks after aligning the embedding subspaces. Experiments on diverse, challenging datasets show that CONE-Align is robust and obtains 19.25% greater accuracy on average than the best-performing state-of-the-art graph alignment algorithm in highly noisy settings.

Network alignment is useful for multiple applications that require increasingly large graphs to be processed. Existing research approaches this as an optimization problem or computes the similarity based on node representations. However, the process of aligning every pair of nodes between relatively large networks is time-consuming and resource-intensive. In this paper, we propose a framework, called G-CREWE (Graph CompREssion With Embedding) to solve the network alignment problem. G-CREWE uses node embeddings to align the networks on two levels of resolution, a fine resolution given by the original network and a coarse resolution given by a compressed version, to achieve an efficient and effective network alignment. The framework first extracts node features and learns the node embedding via a Graph Convolutional Network (GCN). Then, node embedding helps to guide the process of graph compression and finally improve the alignment performance. As part of G-CREWE, we also propose a new compression mechanism called MERGE (Minimum DEgRee NeiGhbors ComprEssion) to reduce the size of the input networks while preserving the consistency in their topological structure. Experiments on all real networks show that our method is more than twice as fast as the most competitive existing methods while maintaining high accuracy.

We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar features. Many popular GNNs fail to generalize to this setting, and are even outperformed by models that ignore the graph structure (e.g., multilayer perceptrons). Motivated by this limitation, we identify a set of key designs—ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations—that boost learning from the graph structure under heterophily. We combine them into a graph neural network, H2GCN, which we use as the base method to empirically evaluate the effectiveness of the identified designs. Going beyond the traditional benchmarks with strong homophily, our empirical analysis shows that the identified designs increase the accuracy of GNNs by up to 40% and 27% over models without them on synthetic and real networks with heterophily, respectively, and yield competitive performance under homophily.

Graph classification is an important problem in many fields, from bioinformatics and neuroscience to computer vision and social network analysis. That said, the task of comparing graphs for the purpose of graph classification faces several major challenges. In particular, an effective graph comparison method must (1) expressively and inductively compare graphs; (2) efficiently compare large graphs; and (3) enable the use of fast machine learning models for graph classification. To address such challenges, we propose Randomized Grid Mapping (RGM), a fast-to-compute feature map that represents a graph via the distribution of its node embeddings in feature space. We justify RGM with close connections to kernel methods: RGM provably approximates the Laplacian kernel mean map and has the multiresolution properties of the pyramid match kernel. We also show that RGM can be extended to incorporate node labels using the Weisfeiler-Lehman framework. Extensive experiments show that graph classification accuracy with RGM feature maps is better than or competitive with many powerful graph kernels, unsupervised graph feature mappings, and deep neural networks. Moreover, comparing graphs based on their node embeddings with RGM is up to an order of magnitude faster than competitive baselines, while maintaining high classification accuracy.

Email is ubiquitous in the workplace. Naturally, machine learning models that make third-party email clients "smarter" can dramatically impact employees' productivity and efficiency. Motivated by this potential, we study the task of professional role inference from email data, which is crucial for email prioritization and contact recommendation systems. The central question we address is: Given limited data about employees, as is common in third-party email applications, can we infer where in the organizational hierarchy these employees belong based on their email behavior? Toward our goal, in this paper we study professional role inference on a unique new email dataset comprising billions of email exchanges across thousands of organizations. Taking a network approach in which nodes are employees and edges represent email communication, we propose EMBER, or EMBedding Email-based Roles, which finds email-centric embeddings of network nodes to be used in professional role inference tasks. EMBER automatically captures behavioral similarity between employees in the email network, leading to embeddings that naturally distinguish employees of different hierarchical roles. EMBER often outperforms the state-of-the-art by 2-20% in role inference accuracy and 2.5-344x in speed. We also use EMBER with our unique dataset to study how inferred professional roles compare between organizations of different sizes and sectors, gaining new insights into organizational hierarchy.

Problems involving multiple networks are prevalent in many scientific and other domains. In particular, network alignment, or the task of identifying corresponding nodes in different networks, has applications across the social and natural sciences. Motivated by recent advancements in node representation learning for single-graph tasks, we propose REGAL (REpresentation learning-based Graph ALignment), a framework that leverages the power of automatically-learned node representations to match nodes across different graphs. Within REGAL we devise xNetMF, an elegant and principled node embedding formulation that uniquely generalizes to multi-network problems. Our results demonstrate the utility and promise of unsupervised representation learning-based network alignment in terms of both speed and accuracy. REGAL runs up to 30x faster in the representation learning stage than comparable methods, outperforms existing network alignment methods by 20 to 30% accuracy on average, and scales to networks with millions of nodes each.

As graph datasets grow, faster data mining methods become indispensable. Random Walk with Restart (RWR), belief propagation, semi-supervised learning, and more graph methods can be expressed as a set of linear equations. In this work, we focus on solving such equations fast and accurately when large number of queries need to be handled. We use RWR as a case study, since it is widely used not only to evaluate the importance of a node, but also as a basis for more complex tasks, e.g., representation learning and community detection. We introduce a new, intuitive two-step divide-and-conquer formulation and a corresponding parallelizable method, FlowR, for solving RWR with two goals: (i) fast and accurate computation under multiple queries; (ii) one-time message exchange between subproblems. We further speed up our proposed method by extending our formulation to carefully designed overlapping subproblems (FlowR-OV) and by leveraging the strengths of iterative methods (FlowR-Hyb). Extensive experiments on synthetic and real networks with up to ∼8 million edges show that our methods are accurate and outperform in runtime various state-of-the-art approaches, running up to 34× faster in preprocessing and up to 32× faster in query time.