With the greater emphasis on privacy and security in our society, the problem of graph unlearning -revoking the influence of specific data on the trained GNN model, is drawing increasing attention. However, ranging from machine unlearning to recently emerged graph unlearning methods, existing efforts either resort to retraining paradigm, or perform approximate erasure that fails to consider the inter-dependency between connected neighbors or imposes constraints on GNN structure, therefore hard to achieve satisfying performance-complexity trade-offs.In this work, we explore the influence function tailored for graph unlearning, so as to improve the unlearning efficacy and efficiency for graph unlearning. We first present a unified problem formulation of diverse graph unlearning tasks w.r.t. node, edge, and feature. Then, we recognize the crux to the inability of traditional influence function for graph unlearning, and devise Graph Influence Function (GIF), a model-agnostic unlearning method that can efficiently and accurately estimate parameter changes in response to a 𝜖-mass perturbation in deleted data. The idea is to supplement the objective of the traditional influence function with an additional loss term of the influenced neighbors due to the structural dependency. Further deductions on the closed-form solution of parameter changes provide a better understanding of the unlearning mechanism. We conduct extensive experiments on four representative GNN models and three benchmark datasets to justify the superiority of GIF for diverse graph unlearning tasks in terms of unlearning efficacy, model utility, and unlearning efficiency. Our implementations are available at https://github.com/wujcan/GIF-torch/.

Thin endometrium has been proven to be a key contributing factor leading to infertility and poor pregnancy outcomes. Increasing the thickness and capacity of thin endometrium seems to be one of the challenging issues in reproductive medicine. The states of qi and blood are closely related to uterine blood circulation. Constitution is regarded as an important basis for determining the incidence as well as distinguishing, preventing, and treating diseases in traditional Chinese medicine. Based on the theory of qi and blood, this paper discusses the constitution factors of thin endometrium and puts forward the prospect of using big data tools to investigate the correlation between qi-blood imbalance constitution and the incidence of thin endometrium, so as to explore new approaches for the prevention and treatment of thin endometrium by regulating qi and blood as well as improving the constitution condition.

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