{
  "id": "2102.05912",
  "version": "v1",
  "published": "2021-02-11T09:56:25.000Z",
  "updated": "2021-02-11T09:56:25.000Z",
  "title": "BoMb-OT: On Batch of Mini-batches Optimal Transport",
  "authors": [
    "Khai Nguyen",
    "Quoc Nguyen",
    "Nhat Ho",
    "Tung Pham",
    "Hung Bui",
    "Dinh Phung",
    "Trung Le"
  ],
  "comment": "36 pages, 18 figures",
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with intractable density, or probability measures with a very high number of supports. The m-OT solves several sparser optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, m-OT is not a proper metric between probability measures since it does not satisfy the identity property. To address this problem, we propose a novel mini-batching scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that can be formulated as a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the proposed BoMb-OT when the regularized parameter goes to infinity. We carry out extensive experiments to show that the new mini-batching scheme can estimate a better transportation plan between two original measures than m-OT. It leads to a favorable performance of BoMb-OT in the matching and color transfer tasks. Furthermore, we observe that BoMb-OT also provides a better objective loss than m-OT for doing approximate Bayesian computation, estimating parameters of interest in parametric generative models, and learning non-parametric generative models with gradient flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-11T09:56:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mini-batches optimal transport",
      "probability measures",
      "sparser optimal transport problems",
      "generative models",
      "mini-batching scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}