Inferring higher-order network structures from nodal data is an emerging challenge across fields such as signal processing, machine learning, and causal inference. While directed acyclic graphs (DAGs) provide a powerful framework for modeling causal or functional dependencies, they only capture pairwise interactions. This paper introduces a new directed acyclic hypergraph (DAH) signal model that generalizes DAG-based structural equation modeling to multi-node (higher-order) relationships. Our approach begins by lifting a directed hyper-graph (DH) into an equivalent bipartite directed graph (DG), where virtual nodes represent source-node sets of hyperedges. Nodal data are assigned to both original and virtual nodes, and an SEM is defined over the DG. By imposing a smooth acyclicity constraint on this bipartite graph, we obtain a continuous and scalable formulation for DAH estimation from nodal observations. The proposed framework unifies hypergraph learning and DAG inference under a common optimization perspective, enabling interpretable higher-order dependency discovery. Numerical experiments demonstrate the ability of the method to recover meaningful DAH structures from simulated nodal data.

This paper addresses graph topology identification for applications where the underlying structure of systems like brain and social networks is not directly observable. Traditional approaches based on signal matching and spectral templates have limitations, particularly in handling scale issues and sparsity assumptions. We introduce a novel covariance matching methodology that efficiently reconstructs the graph topology using observable data. For the structural equation model (SEM) using an undirected graph, we demonstrate that our method can converge to the correct result under relatively soft conditions. Furthermore, we extend our methodology to polynomial models and any known distribution of latent variables, broadening its applicability and utility in diverse graph-based systems.

This paper presents an efficient approach to battery cycle life prediction through few-shot transfer learning, addressing the challenges of costly and limited battery aging data. Leveraging freely available datasets, a multi-layer perceptron (MLP) model was pretrained on diverse battery aging datasets to adapt to new prediction tasks with minimal training samples through few-shot fine-tuning techniques on the target data. The proposed fine-tuning strategy was validated using a heterogeneous aging dataset of 347 batteries, with cycle lives ranging from 144 to 4,052 cycles, incorporating batteries with lithium iron phosphate (LFP), lithium cobalt oxide (LCO), nickel cobalt aluminum oxide (NCA), and nickel manganese cobalt oxide (NMC) chemistries, which ensures robust validation of our methods. The results show that even with few samples of data from a target task, a comparable generalization performance to training from scratch with 100% data can be achieved, thus demonstrating its effectiveness in utilizing available resources for accurate cycle life prediction.