@article{GianniotisKuehnScherbaum2014,
  author    = {Gianniotis, Nikolaos and Kuehn, Nicolas and Scherbaum, Frank},
  title     = {Manifold aligned ground motion prediction equations for regional datasets},
  series = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  volume    = {69},
  journal   = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0098-3004},
  doi       = {10.1016/j.cageo.2014.04.014},
  pages     = {72 -- 77},
  year      = {2014},
  abstract  = {Inferring a ground-motion prediction equation (GMPE) for a region in which only a small number of seismic events has been observed is a challenging task. A response to this data scarcity is to utilise data from other regions in the hope that there exist common patterns in the generation of ground motion that can contribute to the development of a GMPE for the region in question. This is not an unreasonable course of action since we expect regional GMPEs to be related to each other. In this work we model this relatedness by assuming that the regional GMPEs occupy a common low-dimensional manifold in the space of all possible GMPEs. As a consequence, the GMPEs are fitted in a joint manner and not independent of each other, borrowing predictive strength from each other's regional datasets. Experimentation on a real dataset shows that the manifold assumption displays better predictive performance over fitting regional GMPEs independent of each other. (C) 2014 Elsevier Ltd. All rights reserved.},
  language  = {en}
}
@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}
}