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Despite the prevalence of hypergraphs in a variety of high-impact applications, there are relatively few works on hypergraph representation learning, most of which primarily focus on hyperlink prediction, and are often restricted to the transductive learning setting. Among others, a major hurdle for effective hypergraph representation learning lies in the label scarcity of nodes and/or hyperedges. To address this issue, this paper presents an end-to-end, bi-level pre-training strategy with Graph Neural Networks for hypergraphs. The proposed framework named HyperGRL bears three distinctive advantages. First, it is mainly designed in the self-supervised fashion which has broad applicability, and meanwhile it is also capable of ingesting the labeling information when available. Second, at the heart of the proposed HyperGRL are two carefully designed pretexts, one on the node level and the other on the hyperedge level, which enable us to encode both the local and the global context in a mutually complementary way. Third, the proposed framework can work in both transductive and inductive settings. When applying the two proposed pretexts in tandem, it can accelerate the adaptation of the knowledge from the pre-trained model to downstream applications in the transductive setting, thanks to the bi-level nature of the proposed method. Extensive experiments demonstrate that: (1) HyperGRL achieves up to 5.69% improvements in hyperedge classification, and (2) improves pre-training efficiency by up to 42.80% on average 

Cardiac trabeculae are fine rod-like muscles whose ends are attached to the inner walls of ventricles. Accurate extraction of trabeculae is important yet challenging, due to the background noise and limited resolution of cardiac images. Existing works proposed to handle this task by modeling the trabeculae as topological handles for better extraction. Computing optimal representation of these handles is essential yet very expensive. In this work, we formulate the problem as a heuristic search problem, and propose novel heuristic functions based on advanced topological techniques. We show in experiments that the proposed heuristic functions improve the computation in both time and memory. 

We propose a stochastic variational inference algorithm for training large-scale Bayesian networks, where noisy-OR conditional distributions are used to capture higher-order relationships. One application is to the learning of hierarchical topic models for text data. While previous work has focused on two-layer networks popular in applications like medical diagnosis, we develop scalable algorithms for deep networks that capture a multi-level hierarchy of interactions. Our key innovation is a family of constrained variational bounds that only explicitly optimize posterior probabilities for the sub-graph of topics most related to the sparse observations in a given document. These constrained bounds have comparable accuracy but dramatically reduced computational cost. Using stochastic gradient updates based on our variational bounds, we learn noisy-OR Bayesian networks orders of magnitude faster than was possible with prior Monte Carlo learning algorithms, and provide a new tool for understanding large-scale binary data.