Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference
Abstract
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.
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BibTeX
@misc{kilic2026bayesian,
title = {{Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference}},
author = {Afra Kilic and Kim Batselier},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07129},
eprint = {2611.07129},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07129},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference
AU - Afra Kilic
AU - Kim Batselier
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07129
UR - https://arxiv.org/abs/2611.07129
AB - 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.
ER -