{
  "id": "1706.00098",
  "version": "v1",
  "published": "2017-05-31T21:29:40.000Z",
  "updated": "2017-05-31T21:29:40.000Z",
  "title": "Bayesian $l_0$ Regularized Least Squares",
  "authors": [
    "Nicholas G. Polson",
    "Lei Sun"
  ],
  "comment": "21 pages, 6 figures, 1 table",
  "categories": [
    "stat.ML",
    "stat.CO"
  ],
  "abstract": "Bayesian $l_0$-regularized least squares provides a variable selection technique for high dimensional predictors. The challenge in $l_0$ regularization is optimizing a non-convex objective function via search over model space consisting of all possible predictor combinations, a NP-hard task. Spike-and-slab (a.k.a. Bernoulli-Gaussian, BG) priors are the gold standard for Bayesian variable selection, with a caveat of computational speed and scalability. We show that a Single Best Replacement (SBR) algorithm is a fast scalable alternative. Although SBR calculates a sparse posterior mode, we show that it possesses a number of equivalences and optimality properties of a posterior mean. To illustrate our methodology, we provide simulation evidence and a real data example on the statistical properties and computational efficiency of SBR versus direct posterior sampling using spike-and-slab priors. Finally, we conclude with directions for future research.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-31T21:29:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62-04"
    ],
    "keywords": [
      "real data example",
      "sparse posterior mode",
      "high dimensional predictors",
      "single best replacement",
      "sbr calculates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}