用概率张量网络降低非线性系统建模复杂度，自动学习记忆衰减特性。
A Fully Probabilistic Tensor Network for Regularized Volterra System Identification
- 用张量分解压缩伏特拉核，复杂度从O(I^D)降到O(DIR)
- 引入层次先验实现自动秩确定与数据驱动的衰减记忆学习
- 无需额外计算即可获得预测不确定性，适合高维非线性系统建模
用伏特拉级数建模非线性系统时，核系数数量随模型阶数呈指数增长。本文提出贝叶斯张量网络伏特拉核机（BTN-V），将伏特拉核表示为典型多项式分解，使模型复杂度从O(I^D)降至O(DIR)。通过将所有张量成分和超参数视为随机变量，BTN-V在不增加计算成本的前提下提供预测不确定性估计。基于层次稀疏先验，可自动确定秩并直接从数据中学习衰减记忆行为，提升可解释性并防止过拟合。实验表明，该方法具有竞争力的精度、增强的不确定性量化能力及更低的计算开销。
原文摘要 · Abstract (English)
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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