On the Nonasymptotic Scaling Guarantee of Hyperparameter Estimation in Inhomogeneous, Weakly-Dependent Complex Network Dynamical Systems

• URL: http://arxiv.org/abs/2601.15603v1
• Date: Thu, 22 Jan 2026 03:05:39 GMT
• Title: On the Nonasymptotic Scaling Guarantee of Hyperparameter Estimation in Inhomogeneous, Weakly-Dependent Complex Network Dynamical Systems
• Authors: Yi Yu, Yubo Hou, Yinchong Wang, Nan Zhang, Jianfeng Feng, Wenlian Lu,
• Abstract summary: This research proposes the foundational theory to ensure that hierarchical Bayesian methods are statistically consistent for large-scale inhomogeneous systems.<n>Our main result extends this guarantee to the more challenging and realistic setting of weakly-dependent nodes.
• Score: 18.99308667176809
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as the system size grows have been lacking. A critical concern is that hyperparameter estimation may diverge for larger networks, undermining the model's reliability. Formulating the system's evolution in a measure transport perspective, we propose a theoretical framework for estimating hyperparameters with mean-type observations, which are prevalent in many scientific applications. Our primary contribution is a nonasymptotic bound for the deviation of estimate of hyperparameters in inhomogeneous complex network dynamical systems with respect to network population size, which is established for a general family of optimization algorithms within a fixed observation duration. While we firstly establish a consistency result for systems with independent nodes, our main result extends this guarantee to the more challenging and realistic setting of weakly-dependent nodes. We validate our theoretical findings with numerical experiments on two representative models: a Susceptible-Infected-Susceptible model and a Spiking Neuronal Network model. In both cases, the results confirm that the estimation error decreases as the network population size increases, aligning with our theoretical guarantees. This research proposes the foundational theory to ensure that hierarchical Bayesian methods are statistically consistent for large-scale inhomogeneous systems, filling a gap in this area of theoretical research and justifying their application in practice.

Related papers

• From Overfitting to Reliability: Introducing the Hierarchical Approximate Bayesian Neural Network [3.632251954989679]
  HABNN is a novel approach that uses a Gaussian-inverse-Wishart distribution as a hyperprior of the network's weights.<n>Results indicate that HABNN not only matches but often outperforms state-of-the-art models.
  arXiv  Detail & Related papers  (2025-12-15T09:08:42Z)
• Bayesian Neural Networks vs. Mixture Density Networks: Theoretical and Empirical Insights for Uncertainty-Aware Nonlinear Modeling [2.0797819204842036]
  We compare the approaches of Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression.<n>On the theoretical side, we derive convergence rates and error bounds under H"older smoothness conditions, showing that MDNs achieve faster Kullback-Leibler (KL) divergence convergence.<n>Our findings clarify the complementary strengths of posterior-based and likelihood-based probabilistic learning, offering guidance for uncertainty-aware modeling in nonlinear systems.
  arXiv  Detail & Related papers  (2025-10-28T22:00:30Z)
• Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators [0.6117371161379208]
  Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian networks.<n>We propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently accurately predict uncertainties in neural networks.
  arXiv  Detail & Related papers  (2025-07-19T14:57:54Z)
• Latent Diffusion Model Based Denoising Receiver for 6G Semantic Communication: From Stochastic Differential Theory to Application [11.385703484113552]
  We propose a novel semantic communication framework empowered by generative artificial intelligence (GAI)<n>A latent diffusion model (LDM)-based semantic communication framework is proposed that combines a variational autoencoder for semantic features extraction.<n>The proposed system is a training-free framework that supports zero-shot generalization, and achieves superior performance under low-SNR and out-of-distribution conditions.
  arXiv  Detail & Related papers  (2025-06-06T03:20:32Z)
• Certified Neural Approximations of Nonlinear Dynamics [51.01318247729693]
  In safety-critical contexts, the use of neural approximations requires formal bounds on their closeness to the underlying system.<n>We propose a novel, adaptive, and parallelizable verification method based on certified first-order models.
  arXiv  Detail & Related papers  (2025-05-21T13:22:20Z)
• Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks [7.916654052803723]
  This work introduces the Double Neural Network (Double-NN) method to address the problem of individual treatment effect estimation.<n>Deep neural networks are used to model the treatment and control effect functions, while an additional neural network is employed to estimate their parameters.<n> Numerical results highlight the superior performance of the proposed Double-NN method compared to the conformal quantile regression (CQR) method in individual treatment effect estimation.
  arXiv  Detail & Related papers  (2025-05-04T05:40:45Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction [51.82628081279621]
  Multi-modal regression is important in forecasting nonstationary processes or with a complex mixture of distributions. A Structured Radial Basis Function Network is presented as an ensemble of multiple hypotheses predictors for regression problems. It is proved that this structured model can efficiently interpolate this tessellation and approximate the multiple hypotheses target distribution.
  arXiv  Detail & Related papers  (2023-09-02T01:27:53Z)
• A New PHO-rmula for Improved Performance of Semi-Structured Networks [0.0]
  We show that techniques to properly identify the contributions of the different model components in SSNs lead to suboptimal network estimation. We propose a non-invasive post-hocization (PHO) that guarantees identifiability of model components and provides better estimation and prediction quality. Our theoretical findings are supported by numerical experiments, a benchmark comparison as well as a real-world application to COVID-19 infections.
  arXiv  Detail & Related papers  (2023-06-01T10:23:28Z)
• Generalization and Estimation Error Bounds for Model-based Neural Networks [78.88759757988761]
  We show that the generalization abilities of model-based networks for sparse recovery outperform those of regular ReLU networks. We derive practical design rules that allow to construct model-based networks with guaranteed high generalization.
  arXiv  Detail & Related papers  (2023-04-19T16:39:44Z)
• Post-mortem on a deep learning contest: a Simpson's paradox and the complementary roles of scale metrics versus shape metrics [61.49826776409194]
  We analyze a corpus of models made publicly-available for a contest to predict the generalization accuracy of neural network (NN) models. We identify what amounts to a Simpson's paradox: where "scale" metrics perform well overall but perform poorly on sub partitions of the data. We present two novel shape metrics, one data-independent, and the other data-dependent, which can predict trends in the test accuracy of a series of NNs.
  arXiv  Detail & Related papers  (2021-06-01T19:19:49Z)
• Understanding Overparameterization in Generative Adversarial Networks [56.57403335510056]
  Generative Adversarial Networks (GANs) are used to train non- concave mini-max optimization problems. A theory has shown the importance of the gradient descent (GD) to globally optimal solutions. We show that in an overized GAN with a $1$-layer neural network generator and a linear discriminator, the GDA converges to a global saddle point of the underlying non- concave min-max problem.
  arXiv  Detail & Related papers  (2021-04-12T16:23:37Z)
• Network Diffusions via Neural Mean-Field Dynamics [52.091487866968286]
  We propose a novel learning framework for inference and estimation problems of diffusion on networks. Our framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node infection probabilities. Our approach is versatile and robust to variations of the underlying diffusion network models.
  arXiv  Detail & Related papers  (2020-06-16T18:45:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.