In complex and low-data domains such as biomedical research, incorporating background knowledge (BK) graphs, such as protein-protein interaction (PPI) networks, into graph-based machine learning pipelines is a promising research direction. However, while BK is often assumed to improve model performance, its actual contribution and the impact of imperfect knowledge remain poorly understood. In this work, we investigate the role of BK in an important real-world task: cancer subtype classification. Surprisingly, we find that (i) state-of-the-art GNNs using BK perform no better than uninformed models like linear regression, and (ii) their performance remains largely unchanged even when the BK graph is heavily perturbed. To understand these unexpected results, we introduce an evaluation framework, which employs (i) a synthetic setting where the BK is clearly informative and (ii) a set of perturbations that simulate various imperfections in BK graphs. With this, we test the robustness of BK-aware models in both synthetic and real-world biomedical settings. Our findings reveal that careful alignment of GNN architectures and BK characteristics is necessary but holds the potential for significant performance improvements.

In social networks, people influence each other through social links, which can be represented as propagation among nodes in graphs. Influence minimization (IMIN) is the problem of manipulating the structures of an input graph (e.g., removing edges) to reduce the propagation among nodes. IMIN can represent time-critical real-world applications, such as rumor blocking, but IMIN is theoretically difficult and computationally expensive. Moreover, the discrete nature of IMIN hinders the usage of powerful machine learning techniques, which requires differentiable computation. In this work, we propose DiffIM, a novel method for IMIN with two differentiable schemes for acceleration: (1) surrogate modeling for efficient influence estimation, which avoids time-consuming simulations (e.g., Monte Carlo), and (2) the continuous relaxation of decisions, which avoids the evaluation of individual discrete decisions (e.g., removing an edge). We further propose a third accelerating scheme, gradient-driven selection, that chooses edges instantly based on gradients without optimization (spec., gradient descent iterations) on each test instance. Through extensive experiments on real-world graphs, we show that each proposed scheme significantly improves speed with little (or even no) IMIN performance degradation. Our method is Pareto-optimal (i.e., no baseline is faster and more effective than it) and typically several orders of magnitude (spec., up to 15,160X) faster than the most effective baseline while being more effective.

With the recent adoption of laws supporting the ``right to be forgotten'' and the widespread use of Graph Neural Networks for modeling graph-structured data, graph unlearning has emerged as a crucial research area. Current studies focus on the efficient update of model parameters. However, they often overlook the time-consuming re-computation of graph propagation required for each removal, significantly limiting their scalability on large graphs. In this paper, we present ScaleGUN, the first certifiable graph unlearning mechanism that scales to billion-edge graphs. ScaleGUN employs a lazy local propagation method to facilitate efficient updates of the embedding matrix during data removal. Such lazy local propagation can be proven to ensure certified unlearning under all three graph unlearning scenarios, including node feature, edge, and node unlearning. Extensive experiments on real-world datasets demonstrate the efficiency and efficacy of ScaleGUN. Remarkably, ScaleGUN accomplishes $(\epsilon,\delta)=(1,10^{-4})$ certified unlearning on the billion-edge graph ogbn-papers100M in 20 seconds for a $5K$-random-edge removal request -- of which only 5 seconds are required for updating the embedding matrix -- compared to 1.91 hours for retraining and 1.89 hours for re-propagation. Our code is available online.

Core decomposition is an efficient building block for various graph analysis tasks such as dense subgraph discovery and identifying influential nodes. One crucial weakness of the core decomposition is its sensitivity to changes in the graph: inserting or removing a few edges can drastically change the core structure of a graph. Hence, it is essential to characterize, quantify, and, if possible, improve the resilience of the core structure of a given graph in global and local levels. Previous works mostly considered the core resilience of the entire graph or important subgraphs in it. In this work, we study node-based core resilience measures upon edge removals and insertions. We first show that a previously proposed measure, Core Strength, does not correctly capture the core resilience of a node upon edge removals. Next, we introduce the concept of dependency graph to capture the impact of neighbor nodes (for edge removal) and probable future neighbor nodes (for edge insertion) on the core number of a given node. Accordingly, we define Removal Strength and Insertion Strength measures to capture the resilience of an individual node upon removing and inserting an edge, respectively. As naive computation of those measures is costly, we provide efficient heuristics built on key observations about the core structure. We consider two key applications, finding critical edges and identifying influential spreaders, to demonstrate the usefulness of our new measures on various real-world networks and against several baselines. We also show that our heuristic algorithms are more efficient than the naive approaches.

Graph neural networks have shown impressive capabilities in solving various graph learning tasks, particularly excelling in node classification. However, their effectiveness can be hindered by the challenges arising from the widespread existence of noisy measurements associated with the topological or nodal information present in real-world graphs. These inaccuracies in observations can corrupt the crucial patterns within the graph data, ultimately resulting in undesirable performance in practical applications. To address these issues, this paper proposes a novel uncertainty-aware graph learning framework motivated by distributionally robust optimization. Specifically, we use a graph neural network-based encoder to embed the node features and find the optimal node embeddings by minimizing the worst-case risk through a minimax formulation. Such an uncertainty-aware learning process leads to improved node representations and a more robust graph predictive model that effectively mitigates the impact of uncertainty arising from data noise. Our experimental result shows that the proposed framework achieves superior predictive performance compared to the state-of-the-art baselines under various noisy settings.

Influence function, a method from robust statistics, measures the changes of model parameters or some functions about model parameters concerning the removal or modification of training instances. It is an efficient and useful post-hoc method for studying the interpretability of machine learning models without the need for expensive model re-training. Recently, graph convolution networks (GCNs), which operate on graph data, have attracted a great deal of attention. However, there is no preceding research on the influence functions of GCNs to shed light on the effects of removing training nodes/edges from an input graph. Since the nodes/edges in a graph are interdependent in GCNs, it is challenging to derive influence functions for GCNs. To fill this gap, we started with the simple graph convolution (SGC) model that operates on an attributed graph and formulated an influence function to approximate the changes in model parameters when a node or an edge is removed from an attributed graph. Moreover, we theoretically analyzed the error bound of the estimated influence of removing an edge. We experimentally validated the accuracy and effectiveness of our influence estimation function. In addition, we showed that the influence function of an SGC model could be used to estimate the impact of removing training nodes/edges on the test performance of the SGC without re-training the model. Finally, we demonstrated how to use influence functions to guide the adversarial attacks on GCNs effectively.

Causally insufficient structures (models with latent or hidden variables, or with confounding etc.) of joint probability distributions have been subject of intense study not only in statistics, but also in various AI systems. In AI, belief networks, being representations of joint probability distribution with an underlying directed acyclic graph structure, are paid special attention due to the fact that efficient reasoning (uncertainty propagation) methods have been developed for belief network structures. Algorithms have been therefore developed to acquire the belief network structure from data. As artifacts due to variable hiding negatively influence the performance of derived belief networks, models with latent variables have been studied and several algorithms for learning belief network structure under causal insufficiency have also been developed. Regrettably, some of them are known already to be erroneous (e.g. IC algorithm of [Pearl:Verma:91]. This paper is devoted to another algorithm, the Fast Causal Inference (FCI) Algorithm of [Spirtes:93]. It is proven by a specially constructed example that this algorithm, as it stands in [Spirtes:93], is also erroneous. Fundamental reason for failure of this algorithm is the temporary introduction of non-real links between nodes of the network with the intention of later removal. While for trivial dependency structures these non-real links may be actually removed, this may not be the case for complex ones, e.g. for the case described in this paper. A remedy of this failure is proposed.