{
  "id": "1802.08671",
  "version": "v1",
  "published": "2018-02-23T18:40:26.000Z",
  "updated": "2018-02-23T18:40:26.000Z",
  "title": "Langevin Monte Carlo and JKO splitting",
  "authors": [
    "Espen Bernton"
  ],
  "comment": "19 pages. Similar to arxiv:1802.08089",
  "categories": [
    "stat.CO"
  ],
  "abstract": "Algorithms based on discretizing Langevin diffusion are popular tools for sampling from high-dimensional distributions. We develop novel connections between such Monte Carlo algorithms, the theory of Wasserstein gradient flow, and the operator splitting approach to solving PDEs. In particular, we show that a proximal version of the Unadjusted Langevin Algorithm corresponds to a scheme that alternates between solving the gradient flows of two specific functionals on the space of probability measures. Using this perspective, we derive some new non-asymptotic results on the convergence properties of this algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-23T18:40:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "langevin monte carlo",
      "jko splitting",
      "wasserstein gradient flow",
      "monte carlo algorithms",
      "unadjusted langevin algorithm corresponds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}