Pattern Analysis and Applications

, Volume 19, Issue 2, pp 475–485 | Cite as

Approximate variational inference based on a finite sample of Gaussian latent variables

  • Nikolaos GianniotisEmail author
  • Christoph Schnörr
  • Christian Molkenthin
  • Sanjay Singh Bora
Short Paper


Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. marginal likelihood. The lower bound is then optimised with respect to its free parameters, the so-called variational parameters. However, this is not always possible as for certain integrals it is very challenging (or tedious) to come up with a suitable lower bound. Here, we propose a simple scheme that overcomes some of the awkward cases where the usual variational treatment becomes difficult. The scheme relies on a rewriting of the lower bound on the model log-likelihood. We demonstrate the proposed scheme on a number of synthetic and real examples, as well as on a real geophysical model for which the standard variational approaches are inapplicable.


Bayesian inference Posterior estimation Expectation maximisation 



The RESORCE database [1] was used in this work with the kind permission of the SIGMA project. 8 N. Gianniotis was partially funded by the BMBF project “Potsdam Research Cluster for Georisk Analysis, Environmental Change and Sustainability”. C. Molkenthin and S. S. Bora were funded by the graduate research school GeoSim of the Geo.X initiative.9


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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Nikolaos Gianniotis
    • 1
    • 2
    Email author
  • Christoph Schnörr
    • 3
  • Christian Molkenthin
    • 1
  • Sanjay Singh Bora
    • 1
  1. 1.Institute of Earth and Environmental ScienceUniversity of PotsdamPotsdamGermany
  2. 2.Heidelberg Institute for Theoretical Studies, Astroinformatics GroupHeidelbergGermany
  3. 3.Image and Pattern Analysis GroupUniversity of HeidelbergHeidelbergGermany

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