Fast variational inference in the Conjugate Exponential family

[edit]

James Hensman, University of Lancaster
Magnus Rattray, University of Manchester
Neil D. Lawrence, University of Sheffield

in Advances in Neural Information Processing Systems 25

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Abstract

We present a general method for deriving collapsed variational inference algorithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. We exploit the information geometry of the bound to derive much faster optimization methods based on conjugate gradients for these models. Our approach is very general and is easily applied to any model where the mean field update equations have been derived. Empirically we show significant speed-ups for probabilistic models optimized using our bound.


@InProceedings{hensman-fast12,
  title = 	 {Fast variational inference in the Conjugate Exponential family},
  author = 	 {James Hensman and Magnus Rattray and Neil D. Lawrence},
  booktitle = 	 {Advances in Neural Information Processing Systems},
  year = 	 {2012},
  editor = 	 {Peter L. Bartlett and Fernando C. N. Pereira and Christopher J. C. Burges and Léon Bottou and Kilian Q. Weinberger},
  volume = 	 {25},
  address = 	 {Cambridge, MA},
  month = 	 {00},
  edit = 	 {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2012-01-01-hensman-fast12.md},
  url =  	 {http://inverseprobability.com/publications/hensman-fast12.html},
  abstract = 	 {We present a general method for deriving collapsed variational inference algorithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. We exploit the information geometry of the bound to derive much faster optimization methods based on conjugate gradients for these models. Our approach is very general and is easily applied to any model where the mean field update equations have been derived. Empirically we show significant speed-ups for probabilistic models optimized using our bound.},
  crossref =  {Bartlett:nips12},
  key = 	 {Hensman:fast12},
  linkpdf = 	 {http://papers.nips.cc/paper/4766-fast-variational-inference-in-the-conjugate-exponential-family},
  OPTgroup = 	 {}

}
%T Fast variational inference in the Conjugate Exponential family
%A James Hensman and Magnus Rattray and Neil D. Lawrence
%B 
%C Advances in Neural Information Processing Systems
%D 
%E Peter L. Bartlett and Fernando C. N. Pereira and Christopher J. C. Burges and Léon Bottou and Kilian Q. Weinberger
%F hensman-fast12	
%P --
%R 
%U http://inverseprobability.com/publications/hensman-fast12.html
%V 25
%X We present a general method for deriving collapsed variational inference algorithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. We exploit the information geometry of the bound to derive much faster optimization methods based on conjugate gradients for these models. Our approach is very general and is easily applied to any model where the mean field update equations have been derived. Empirically we show significant speed-ups for probabilistic models optimized using our bound.
TY  - CPAPER
TI  - Fast variational inference in the Conjugate Exponential family
AU  - James Hensman
AU  - Magnus Rattray
AU  - Neil D. Lawrence
BT  - Advances in Neural Information Processing Systems
PY  - 2012/01/01
DA  - 2012/01/01
ED  - Peter L. Bartlett
ED  - Fernando C. N. Pereira
ED  - Christopher J. C. Burges
ED  - Léon Bottou
ED  - Kilian Q. Weinberger	
ID  - hensman-fast12	
SP  - 
EP  - 
L1  - http://papers.nips.cc/paper/4766-fast-variational-inference-in-the-conjugate-exponential-family
UR  - http://inverseprobability.com/publications/hensman-fast12.html
AB  - We present a general method for deriving collapsed variational inference algorithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. We exploit the information geometry of the bound to derive much faster optimization methods based on conjugate gradients for these models. Our approach is very general and is easily applied to any model where the mean field update equations have been derived. Empirically we show significant speed-ups for probabilistic models optimized using our bound.
ER  -

Hensman, J., Rattray, M. & Lawrence, N.D.. (2012). Fast variational inference in the Conjugate Exponential family. Advances in Neural Information Processing Systems 25:-