{
  "id": "1403.4359",
  "version": "v2",
  "published": "2014-03-18T06:55:50.000Z",
  "updated": "2014-09-05T17:38:55.000Z",
  "title": "Pre-processing for approximate Bayesian computation in image analysis",
  "authors": [
    "Matthew T. Moores",
    "Kerrie Mengersen",
    "Christian P. Robert"
  ],
  "comment": "5th IMS-ISBA joint meeting (MCMSki IV)",
  "categories": [
    "stat.CO"
  ],
  "abstract": "Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 hours to only 7 minutes. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-18T06:55:50.000Z",
      "abstract": "The existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. The dimension of the state vector in this model is equal to the size of the data, which can be millions of pixels. We introduce a preparatory computation step before model fitting to improve the scalability of ABC. The output of this pre-computation can be reused across multiple datasets. We illustrate this method by estimating the smoothing parameter for satellite images, demonstrating that the pre-computation step can reduce the average runtime required for model fitting from 46 hours to only 21 minutes.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-05T17:38:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62F15",
      "G.3",
      "I.4.6",
      "I.5.1"
    ],
    "keywords": [
      "approximate bayesian computation",
      "image analysis",
      "preparatory computation step",
      "high dimensional data",
      "potts model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.4359M"
    }
  }
}