Spatio-Temporal Structured Sparse Regression with Hierarchical Gaussian Process Priors

Danil Kuzin, Olga Isupova, Lyudmila Mihaylova

Research output: Contribution to journalArticle

Abstract

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies between the components of the sparse signal of interest. A hierarchical Gaussian process describes such structure and the interdependencies are represented via the covariance matrices of the prior distributions. The inference is based on the expectation propagation method and the theoretical derivation of the posterior distribution is provided in this paper. The inference framework is thoroughly evaluated over synthetic, real video, and electroencephalography (EEG) data where the spatio-temporal evolving patterns need to be reconstructed with high accuracy. It is shown that it achieves 15% improvement of the F-measure compared with the alternating direction method of multipliers, spatio-temporal sparse Bayesian learning method and the one-level Gaussian process model. Additionally, the required memory for the proposed algorithm is less than in the one-level Gaussian process model. This structured sparse regression framework is of broad applicability to source localization and object detection problems with sparse signals.

Original languageEnglish
Pages (from-to)4598-4611
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume66
Issue number17
Early online date23 Jul 2018
DOIs
Publication statusPublished - 1 Sep 2018

Keywords

  • Bayes methods
  • biomedical imaging
  • Compressed sensing
  • Gaussian processes
  • object detection

Cite this

Spatio-Temporal Structured Sparse Regression with Hierarchical Gaussian Process Priors. / Kuzin, Danil; Isupova, Olga; Mihaylova, Lyudmila.

In: IEEE Transactions on Signal Processing, Vol. 66, No. 17, 01.09.2018, p. 4598-4611.

Research output: Contribution to journalArticle

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