To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without incurring exponential computational cost. However, extending this model to a fully probabilistic formulation introduces several design challenges. In particular, for tensor train (TT) models, it is unclear which TT-core should be treated in a Bayesian manner. We introduce a Bayesian tensor train kernel machine that applies Laplace approximation to estimate the posterior distribution over a selected TT-core and employs variational inference (VI) for precision hyperparameters. Experiments show that core selection is largely independent of TT-ranks and feature structure, and that VI replaces cross-validation while offering up to 65x faster training. The method's effectiveness is demonstrated on an inverse dynamics problem.

翻译：为解决高斯过程回归的可扩展性限制，已有多种近似技术被提出。其中一种基于张量网络的方法，能够利用指数级数量的基函数而无需承担指数级计算成本。然而，将该模型扩展为完全概率化形式引入了若干设计挑战。特别是对于张量列车模型，尚不清楚应将哪个TT核以贝叶斯方式处理。我们提出了一种贝叶斯张量列车核机器，该方法应用拉普拉斯近似来估计选定TT核的后验分布，并采用变分推断处理精度超参数。实验表明，核选择基本独立于TT秩和特征结构，且变分推断可替代交叉验证，同时实现高达65倍的训练加速。该方法在逆动力学问题上的有效性得到了验证。