A Fully Probabilistic Tensor Network for Regularized Volterra System Identification

• URL: http://arxiv.org/abs/2511.20457v1
• Date: Tue, 25 Nov 2025 16:24:52 GMT
• Title: A Fully Probabilistic Tensor Network for Regularized Volterra System Identification
• Authors: Afra Kilic, Kim Batselier,
• Abstract summary: This work introduces Bayesian Network Volterra kernel machines (BTN-V)<n>BTN-V represents Volterra kernels using canonical polyadic decomposition, reducing model complexity from O(ID) to O(DIR)
• Score: 6.101839518775971
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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