← 研踪 PaperTrailarXiv:2611.07129 · v1
Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference
首次提交 2026-11-05 04:54
版本更新 2026-11-05 04:54
雷达观测 2026-11-06 10:04
摘要
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.
作者备注：31 pages, 4 figures, 1 algorithm. Code available at https://github.com/afrakilic/BTTKM
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v1 · 2026-11-05 04:54 · 最新观测版本
Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference
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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