Variational Approximations for Frequentist and Bayesian Inference

Luca Maestrini

Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

Luca Maestrini

Last modified: 2018-05-22

Abstract

Variational approximations are a flexible instrument for deterministic approximate inference in complex statistical models. We illustrate the concept of variational approximation from both frequentist and Bayesian perspectives, providing methodological examples that take advantage of the classical concepts of exponential families.

References

\bibitem{AzzaliniCapitanio2003} Azzalini, A., Capitanio, A.: Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. R. Stat. Soc. Ser. B. \textbf{65}, 367--389 (2003)

\bibitem{Jordan2004} Jordan, M. I.: Graphical Models. Stat. Sci. \textbf{19}, 140--155 (2004)

\bibitem{Minka2005} Minka, T.: Divergence measures and message passing. Microsoft Res. Tech. Rep. Ser. \textbf{173}, 1--17 (2005)

\bibitem{OrmerodWand2010} Ormerod, J. T., Wand, M. P.: Explaining variational approximations. Am. Stat. \textbf{64}, 140--153 (2010)

\bibitem{OrmerodWand2012} Ormerod, J. T., Wand, M. P.: Gaussian variational approximate inference for generalized linear mixed models. J. Comput. Graph. Stat. \textbf{21}, 2--17 (2012)

\bibitem{OSullivan1988} O'Sullivan, F.: Nonparametric estimation of relative risk using splines and cross-validation. J. Sci. Stat. Comput. \textbf{9}, 531--542 (1988)

\bibitem{StanDevelopmentTeam2018}Stan Development Team: rStan: the R interface to Stan. R package version 2.17.3.http://mc-stan.org/ (2018)

\bibitem{Wand2017} Wand, M. P.: Fast approximate inference for arbitrarily large semiparametric regression models via message passing. J. Am. Stat. Assoc. \textbf{112}, 137--168 (2017)

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