Tensor network kernel machines (TNKMs) combine nonlinear features with low-rank tensor representations to model complex relationships efficiently. However, selecting an appropriate tensor rank remains challenging, as conventional rank-search methods require training multiple candidate models, increasing computational costs. In this work, we focus on a canonical polyadic (CP) tensor network parameterization and propose GB-CPKM, a gradient boosting framework that builds a higher-capacity predictor by sequentially adding fixed-rank learners. This approach provides a new perspective on rank selection by incrementally increasing model capacity, with ensemble size selected based on validation performance rather than through explicit rank search. Experiments on real-world regression benchmarks show that GB-CPKM trains up to 6x faster and uses up to 2x less peak memory than a conventional rank-selection method based on cross-validation, while achieving comparable predictive performance. These results highlight the potential of gradient boosting to improve the computational efficiency and scalability of tensor-network learning.
Tensor Network (TN) kernel machines accelerate supervised learning by using low-rank TNs to reduce computation and memory. However, most TN-based methods are deterministic with manually tuned ranks and feature dimensions, while the existing Bayesian TN kernel machine is restricted to the CANDECOMP/PARAFAC decomposition (CPD), whose single rank is shared by all modes. We extend this framework to the tensor train (TT) and propose Bayesian Tensor Train Kernel Machines (BTT-KM), whose hierarchical ARD-type priors on the TT cores infer the TT ranks and feature dimensions from data. Since each TT core is coupled to the others only through its neighbors, its closed-form posterior update requires propagating the contributions of all other cores along the chain. Mean-field variational inference yields a Bayesian alternating least squares algorithm with the same computational complexity as its deterministic counterpart and a closed-form predictive distribution. A synthetic experiment illustrates that BTT-KM recovers the true TT ranks and feature dimensions from an over-parameterized initialization.