Bayesian inference for spatio-temporal spike-and-slab priors

Michael Riis Andersen, Aki Vehtari, Ole Winther, Lars Kai Hansen

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
25 Downloads (Pure)

Abstract

In this work, we address the problem of solving a series of underdetermined linear inverse problemblems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets.

Original languageEnglish
Pages (from-to)1-58
JournalJournal of Machine Learning Research
Volume18
Publication statusPublished - 1 Dec 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Bayesian inference
  • Expectation propagation
  • Linear inverse problems
  • Sparsity-promoting priors
  • Spike-and-slab priors

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