Variational Estimation in Spatiotemporal Systems From Continuous and Point-Process Observations

A. Zammit-Mangion, G. Sanguinetti, V. Kadirkamanathan

Research output: Contribution to journalArticlepeer-review

Abstract

Spatiotemporal models are ubiquitous in science and engineering, yet estimation in these models from discrete observations remains computationally challenging. We propose a practical novel approach to inference in spatiotemporal processes, both from continuous and from discrete (point-process) observations. The method is based on a finite-dimensional reduction of the spatiotemporal model, followed by a mean field variational approximate inference approach. To cater for the point-process case, a variational-Laplace approach is proposed which yields tractable computations of approximate variational posteriors. Results show that variational Bayes is a viable and practical alternative to statistical methods such as expectation maximization or Markov chain Monte Carlo.
Original languageEnglish
Pages (from-to)3449-3459
Number of pages11
JournalIEEE Transactions on Signal Processing
Volume60
Issue number7
DOIs
Publication statusPublished - 1 Jul 2012

Keywords

  • Bayes methods
  • approximation theory
  • differential equations
  • spatiotemporal phenomena
  • variational techniques
  • Markov chain Monte Carlo method
  • continuous observations
  • discrete observations
  • expectation maximization method
  • finite-dimensional reduction
  • mean field variational approximation inference approach
  • point-process observations
  • spatiotemporal systems
  • variational Bayes method
  • variational estimation
  • variational posteriors approximation
  • variational-Laplace approach
  • Approximation methods
  • Equations
  • Mathematical model
  • Moment methods
  • Sensors
  • Spatiotemporal phenomena
  • Stochastic processes
  • Dynamic spatiotemporal modeling
  • spatiotemporal point-processes
  • stochastic partial differential equations
  • variational Bayes
  • variational-Laplace

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