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Hypergraphs are instrumental in modeling complex relational systems that encompass a wide spectrum of high-order interactions among components. One prevalent analysis task is the properties estimation of large-scale hypergraphs, which involves selecting a subset of nodes and hyperedges while preserving the characteristics of the entire hypergraph. This paper aims to sample hypergraphs via random walks and is the first to perform unbiased random walks for sampling of nodes and hyperedges simultaneously in large-scale hypergraphs to the best of our knowledge. Initially, we analyze the stationary distributions of nodes and hyperedges for the simple random walk, and show that there is a high bias in both nodes and hyperedges. Subsequently, to eliminate the high bias of the simple random walk, we propose unbiased random walk strategies for nodes and hyperedges, respectively. Finally, a single joint walk schema is developed for sampling nodes and hyperedges simultaneously. To accelerate the convergence process, we employ delayed acceptance and history-aware techniques to assist our algorithm in achieving fast convergence. Extensive experimental results validate our theoretical findings, and the unbiased sampling algorithms for nodes and hyperedges have their complex hypergraph scenarios for which they are applicable. The joint random walk algorithm balanced the sampling applicable to both nodes and hyperedges. [ABSTRACT FROM AUTHOR]

In the resource-constrained federated edge learning (FEEL) systems, fragment-sharing is an efficient approach for multiple clients to cooperatively train a giant model with billions of parameters. Compared with the classical federated learning schemes where the local model is fully trained and exchanged by each client, the fragment-sharing only requires each client to optionally choose a parameter-fragment to train and share, according to its storage, computing, and networking abilities. However, when the full model is no longer delivered in fragment-sharing, the backdoor attacks hidden behind the fragments become harder to be detected, which introduces formidable challenge for the security of FEEL systems. In this paper, we firstly show that the existing fragment-sharing works suffer a lot from the backdoor attacks. Then, a Backdoor-Resilient approach, named BR-FEEL, is introduced to defend against the potential backdoor attacks. Specifically, a twin model is built by each benign client to integrate the parameter-fragments from others. A knowledge distillation process is designed on each client to transfer the clean knowledge from its twin model to local model. With the twin model and knowledge distillation process, our BR-FEEL approach makes sure that the local models of the benign clients will not be backdoored. Experiments on CIFAR-10 and GTSRB datasets with MobileNetV2 and ResNet-34 are conducted. The numerical results demonstrate the efficacy of BR-FEEL on reducing attack success rates by over 90% compared to other baselines under various attack methods. [ABSTRACT FROM AUTHOR]