{
  "id": "2310.20630",
  "version": "v1",
  "published": "2023-10-31T16:59:07.000Z",
  "updated": "2023-10-31T16:59:07.000Z",
  "title": "Projecting basis functions with tensor networks for Gaussian process regression",
  "authors": [
    "Clara Menzen",
    "Eva Memmel",
    "Kim Batselier",
    "Manon Kok"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on the total number of basis functions $M$. We develop an approach that allows us to use an exponential amount of basis functions without the corresponding exponential computational complexity. The key idea to enable this is using low-rank TNs. We first find a suitable low-dimensional subspace from the data, described by a low-rank TN. In this low-dimensional subspace, we then infer the weights of our model by solving a Bayesian inference problem. Finally, we project the resulting weights back to the original space to make GP predictions. The benefit of our approach comes from the projection to a smaller subspace: It modifies the shape of the basis functions in a way that it sees fit based on the given data, and it allows for efficient computations in the smaller subspace. In an experiment with an 18-dimensional benchmark data set, we show the applicability of our method to an inverse dynamics problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-31T16:59:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian process regression",
      "projecting basis functions",
      "tensor networks",
      "low-rank tn",
      "smaller subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}