---
title: "Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.07129v1"
permalink: "https://feed.astralor.com/items/itm_f89e4d94d5227a953fdfb62c"
published: "2026-11-04T20:54:46.000Z"
score: 56
channel: "tech"
tags: ["推理效率","Bayesian Tensor Train","Kernel Machines","Automatic Model Complexity","Inference Tensor Network","TNs","However","TN-based"]
---

# Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference

## 速览

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 dimension…

## 关键点

- 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 r…
- 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.

## 全文

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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