Uncovering the underlying complex network structure with high-order topologies from observational data is a fundamental challenge across diverse domains. Can we provide a versatile and precise approach for inferring full-order structure solely from node states? To address this issue, we propose a data-driven likelihood optimization framework for reconstructing the underlying topological structures. Our approach captures state transition relationships in binary time series generated by Markovian dynamics and employs the difference of convex algorithm to efficiently handle the optimization problem of full-order reconstruction. Experiments demonstrate that our approach excels in reconstructing a full-order simplicial network and achieves high accuracy across different experimental conditions, highlighting its potential to uncover complex interactions.

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• Network inference