{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07129",
  "author_total": 2,
  "authors": [
    {
      "name": "Afra Kilic"
    },
    {
      "name": "Kim Batselier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/69ss2fm0j9vcj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07129",
  "fulltext_url": null,
  "id": "69ss2fm0j9vcj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07129",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/69ss2fm0j9vcj.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:40Z",
      "native_id": "2611.07129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07129"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference",
  "title_text": "Bayesian Tensor Train Kernel Machines with Automatic Model Complexity Inference",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:27Z",
  "url": "https://research.draconitic.com/paper/69ss2fm0j9vcj",
  "venue": "arXiv",
  "versions": []
}