TY  - JOUR
A1  - Gianniotis, Nikolaos
A1  - Schnoerr, Christoph
A1  - Molkenthin, Christian
A1  - Bora, Sanjay Singh
T1  - Approximate variational inference based on a finite sample of Gaussian latent variables
JF  - Pattern Analysis & Applications
N2  - 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.
KW  - Bayesian inference
KW  - Posterior estimation
KW  - Expectation maximisation
Y1  - 2016
U6  - https://doi.org/10.1007/s10044-015-0496-9
SN  - 1433-7541
SN  - 1433-755X
VL  - 19
SP  - 475
EP  - 485
PB  - Springer
CY  - New York
ER  - 
TY  - THES
A1  - Molkenthin, Christian
T1  - Sensitivity analysis in seismic Hazard assessment using algorithmic differentiation
Y1  - 2016
ER  -