Reconstruction of 3-simplex based on Bayesian inference

Existing network reconstruction studies have primarily focused on interactions involving 2-simplex or lower dimensions. However, with the growing interest in higher-order or many-body interaction networks, reconstructing such structures from observational data presents significant challenges. We propose a Bayesian method for 3-simplex reconstruction to extend network reconstruction to higher dimensions. This approach integrates prior knowledge with observational data to effectively handle noise and uncertainty, enabling stable and accurate inference of latent higher-order interactions in networks. Simulation studies and an empirical analysis of the comment network related to the Weibo topic “DeepSeek has surprised some people in the US” validate the accuracy and robustness of the proposed method. Our work extends network reconstruction to higher-order structures and provides a general framework for reconstructing complex higher-order interactions in real-world networks.