Understanding how functional dynamics emerge from the brain’s underlying structural architecture remains a fundamental challenge in neuroscience. Conventional graph diffusion (GD) models are limited by sparse anatomical connectivity, leading to a failure to capture indirect connectivity and negatively correlated relationships. To overcome these challenges, we introduce hypergraphs and deep neural networks to enhance the representation of brain connectivity. Specifically, graphs and hypergraphs are integrated to construct a connected-graph, providing a comprehensive representation of inter-regional brain connectivity. The Fourier-induced deep neural network is employed to infer latent inter-regional relationships from structural connectivity by leveraging spectral features, effectively capturing both low- and high-frequency components. These deduced relationships are incorporated into the connected-graph, giving rise to a connected-graph diffusion (CD) model, which is further refined via eigen-decomposition to form an eigen-based connected-graph diffusion (ECD) model. Evaluated on 1012 subjects from the Human Connectome Project (HCP) S1200 release, the ECD model achieves a mean Pearson correlation coefficients of 0.7230 in functional connectivity (FC) prediction, outperforming the GD model (0.5513) and CD model (0.6518). The stability analysis demonstrates that the prediction of the ECD model is reliable. This work demonstrates that integrating biological mechanisms with machine learning methods can accurately model complex brain networks, with implications for neural signal processing, brain-inspired computing, and neuropsychiatric diagnosis.

Abstract Prediction problems regularly exist in practical application problems, where real application systems are usually complex. For multi-model data in complex systems, effectively identifying the patterns of each data set is significant for subsequent prediction. This paper focuses on the prediction problem of multi-model data and proposes an adaptive regression algorithm (CFM-MSVR) that combines a clustering feedback mechanism with improved support vector regression. The clustering feedback mechanism (CFM) clusters samples based on their residuals in each forecasting model, enabling the discovery of original data generation models. Meanwhile, it can intelligently estimate the number of clusters based on the number of samples in each cluster, reducing computational cost and dependence on empirical settings. In the regression stage, the multi-model support vector regression (MSVR) leverages the non-dominated sorting genetic algorithm II (NSGA-II) to optimise the parameters of the support vector regression, thereby improving the generalisation of each sub-model. The proposed method is evaluated on a simulated dataset, four real-world datasets, and the 2012 Global Energy Forecasting Competition dataset. Results show that CFM-MSVR achieves a MAPE% of 1.52 on the energy prediction task, demonstrating its strong performance in complex forecasting scenarios.

Semiparametric statistics play a pivotal role in a wide range of domains, including but not limited to missing data, causal inference, and transfer learning, to name a few. In many settings, semiparametric theory leads to (nearly) statistically optimal procedures that yet involve numerically solving Fredholm integral equations of the second kind. Traditional numerical methods, such as polynomial or spline approximations, are difficult to scale to multi-dimensional problems. Alternatively, statisticians may choose to approximate the original integral equations by ones with closed-form solutions, resulting in computationally more efficient, but statistically suboptimal or even incorrect procedures. To bridge this gap, we propose a novel framework by formulating the semiparametric estimation problem as a bi-level optimization problem; and then we propose a scalable algorithm called Deep Neural-Nets Assisted Semiparametric Estimation ($\mathsf{DNA\mbox{-}SE}$) by leveraging the universal approximation property of Deep Neural-Nets (DNN) to streamline semiparametric procedures. Through extensive numerical experiments and a real data analysis, we demonstrate the numerical and statistical advantages of $\mathsf{DNA\mbox{-}SE}$ over traditional methods. To the best of our knowledge, we are the first to bring DNN into semiparametric statistics as a numerical solver of integral equations in our proposed general framework.