{"ID":2837038,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20457","arxiv_id":"2511.20457","title":"A Fully Probabilistic Tensor Network for Regularized Volterra System Identification","abstract":"Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the Bayesian Tensor Network framework to Volterra system identification. BTN-V represents Volterra kernels using canonical polyadic decomposition, reducing model complexity from O(I^D) to O(DIR). By treating all tensor components and hyperparameters as random variables, BTN-V provides predictive uncertainty estimation at no additional computational cost. Sparsity-inducing hierarchical priors enable automatic rank determination and the learning of fading-memory behavior directly from data, improving interpretability and preventing overfitting. Empirical results demonstrate competitive accuracy, enhanced uncertainty quantification, and reduced computational cost.","short_abstract":"Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the Bayesian Tensor Network framework to Volterra system identification. BTN-V repre...","url_abs":"https://arxiv.org/abs/2511.20457","url_pdf":"https://arxiv.org/pdf/2511.20457v1","authors":"[\"Afra Kilic\",\"Kim Batselier\"]","published":"2025-11-25T16:24:52Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}