@article{GianniotisSchnoerrMolkenthinetal.2016,
  author    = {Gianniotis, Nikolaos and Schnoerr, Christoph and Molkenthin, Christian and Bora, Sanjay Singh},
  title     = {Approximate variational inference based on a finite sample of Gaussian latent variables},
  series = {Pattern Analysis \& Applications},
  volume    = {19},
  journal   = {Pattern Analysis \& Applications},
  publisher = {Springer},
  address   = {New York},
  issn      = {1433-7541},
  doi       = {10.1007/s10044-015-0496-9},
  pages     = {475 -- 485},
  year      = {2016},
  abstract  = {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.},
  language  = {en}
}