Affine independent variational inference

Advances in Neural Information Processing Systems

Volumn 3, Issue , 2012, Pages 2186-2194

  Challis, Edward ^a   Barber, David ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AFFINE TRANSFORMATIONS; GENERALISED LINEAR MODELS; KULLBACK LEIBLER DIVERGENCE; LATENT VARIABLE; PROBABILISTIC MODELS; TARGET DENSITY; VARIATIONAL APPROXIMATION; VARIATIONAL INFERENCE;

FAST FOURIER TRANSFORMS;

EID: 84877742737     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (28)

1. D. Barber. Bayesian Reasoning and Machine Learning. Cambridge University Press, 2012.
2. D. Barber and C. M. Bishop. Ensemble Learning for Multi-Layer Networks. In Advances in Neural Information Processing Systems, NIPS 10, 1998.
3. D. Bickson and C. Guestrin. Inference with Multivariate Heavy-Tails in Linear Models. In Advances in Neural Information Processing Systems, NIPS 23. 2010.
4. C. M. Bishop, N. Lawrence, T. Jaakkola, and M. I. Jordan. Approximating Posterior Distributions in Belief Networks Using Mixtures. In Advances in Neural Information Processing Systems, NIPS 10, 1998.
5. G. Bouchard and O. Zoeter. Split Variational Inference. In International Conference on Artificial Intelligence and Statistics, AISTATS, 2009.
6. R. N. Bracewell. The Fourier Transform and its Applications. McGraw-Hill Book Co, Singapore, 2000.
7. E. Challis and D. Barber. Concave Gaussian Variational Approximations for Inference in Large-Scale Bayesian Linear Models. In International Conference on Artificial Intelligence and Statistics, AISTATS, 2011.
8. T. M. Cover and J. A. Thomas. Elements of Information Theory. Wiley, New York, 1991.
9. J. T. A. S. Ferreira and M. F. J. Steel. A New Class of Skewed Multivariate Distributions with Applications To Regression Analysis. Statistica Sinica, 17:505-529, 2007.
10. G. Gersman, M. Hoffman, and D. Blei. Nonparametric Variational Inference. In International Conference on Machine Learning, ICML 29, 2012.
11. M. Girolami. A Variational Method for Learning Sparse and Overcomplete Representations. Neural Computation, 13:2517-2532, 2001.
12. A. Graves. Practical Variational Inference for Neural Networks. In Advances in Neural Information Processing Systems, NIPS 24, 2011.
13. A. Honkela and H. Valpola. Unsupervised Variational Bayesian Learning of Nonlinear Models. In Advances in Neural Information Processing Systems, NIPS 17, 2005.
14. T. Jaakkola and M. Jordan. A Variational Approach to Bayesian Logistic Regression Problems and their Extensions. In Artificial Intelligence and Statistics, AISTATS 6, 1996.
15. M. E. Khan, B. Marlin, G. Bouchard, and K. Murphy. Variational Bounds for Mixed-Data Factor Analysis. In Advances in Neural Information Processing Systems, NIPS 23, 2010.
16. D. A. Knowles and T. Minka. Non-conjugate Variational Message Passing for Multinomial and Binary Regression. In Advances in Neural Information Processing Systems, NIPS 23. 2011.
17. M. Kuss. Gaussian Process Models for Robust Regression, Classification, and Reinforcement Learning. PhD thesis, Technische Universität Darmstadt, Darmstadt, Germany, 2006.
18. H. Nickisch and M. Seeger. Convex Variational Bayesian Inference for Large Scale Generalized Linear Models. In International Conference on Machine Learning, ICML 26, 2009.
19. J. P. Nolan. Stable Distributions - Models for Heavy Tailed Data. Birkhauser, Boston, 2012. In progress, Chapter 1 online at academic2.american. edu/~jpnolan.
20. M. Opper and C. Archambeau. The Variational Gaussian Approximation Revisited. Neural Computation, 21(3):786-792, 2009.
21. J. Ormerod. Skew-Normal Variational Approximations for Bayesian Inference. Technical Report CRGTR-93-1, School of Mathematics and Statistics, University of Sydney, 2011.
22. A. Palmer, D.Wipf, K. Kreutz-Delgado, and B. Rao. Variational EM Algorithms for Non-Gaussian Latent Variable Models. In Advances in Neural Information Processing Systems, NIPS 20, 2006.
23. C. E. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, 2006.
24. P. Ruckdeschel and M. Kohl. General Purpose Convolution Algorithm in S4-Classes by means of FFT. Technical Report 1006.0764v2, arXiv.org, 2010.
25. S. K. Sahu, D. K. Dey, and M. D. Branco. A New Class of Multivariate Skew Distributions with Applications to Bayesian Regression Models. The Canadian Journal of Statistics / La Revue Canadienne de Statistique, 31(2):129-150, 2003.
26. P. Schaller and G. Temnov. Efficient and precise computation of convolutions: applying FFT to heavy tailed distributions. Computational Methods in Applied Mathematics, 8(2):187-200, 2008.
27. C. Siddhartha, F. Nardari, and N. Shephard. Markov chain Monte Carlo methods for stochastic volatility models. Journal of Econometrics, 108(2):281-316, 2002.
28. M. J. Wainwright and M. I. Jordan. Graphical Models, Exponential Families, and Variational Inference. Foundations and Trends in Machine Learning, 1(1-2):1-305, 2008.