{
  "id": "1406.4993",
  "version": "v2",
  "published": "2014-06-19T10:01:15.000Z",
  "updated": "2015-06-30T10:59:00.000Z",
  "title": "Divide-and-Conquer with Sequential Monte Carlo",
  "authors": [
    "Fredrik Lindsten",
    "Adam M. Johansen",
    "Christian A. Naesseth",
    "Bonnie Kirkpatrick",
    "Thomas B. Schön",
    "John Aston",
    "Alexandre Bouchard-Côté"
  ],
  "categories": [
    "stat.CO",
    "stat.ML"
  ],
  "abstract": "We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured decomposition of the model of interest, turning the overall inferential task into a collection of recursively solved sub-problems. The proposed method is applicable to a broad class of probabilistic graphical models, including models with loops. Unlike a standard SMC sampler, the proposed Divide-and-Conquer SMC employs multiple independent populations of weighted particles, which are resampled, merged, and propagated as the method progresses. We illustrate empirically that this approach can outperform standard methods in terms of the accuracy of the posterior expectation and marginal likelihood approximations. Divide-and-Conquer SMC also opens up novel parallel implementation options and the possibility of concentrating the computational effort on the most challenging sub-problems. We demonstrate its performance on a Markov random field and on a hierarchical logistic regression problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-19T10:01:15.000Z",
      "abstract": "We develop a Sequential Monte Carlo (SMC) procedure for inference in probabilistic graphical models using the divide-and-conquer methodology. The method is based on an auxiliary tree-structured decomposition of the model of interest turning the overall inferential task into a collection of recursively solved sub-problems. Unlike a standard SMC sampler, the proposed method employs multiple independent populations of weighted particles, which are resampled, merged, and propagated as the method progresses. We illustrate empirically that this approach can outperform standard methods in estimation accuracy. It also opens up novel parallel implementation options and the possibility of concentrating the computational effort on the most challenging sub-problems. The proposed method is applicable to a broad class of probabilistic graphical models. We demonstrate its performance on a Markov random field and on a hierarchical Bayesian model.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-30T10:59:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sequential monte carlo",
      "divide-and-conquer",
      "probabilistic graphical models",
      "method employs multiple independent populations",
      "novel parallel implementation options"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.4993L"
    }
  }
}