## Approximate Inference |

See also Monte Carlo Methods.

**Some relevant publications:**

- Heller, K.A. and Ghahramani, Z. (2005)

Bayesian Hierarchical Clustering,

Gatsby Unit Technical Report GCNU-TR 2005-002. [ps] [pdf]

A shorter version was published in the*Twenty-second International Conference on Machine Learning***(ICML-2005)**. [pdf] - Snelson, E., and Ghahramani, Z. (2005)

Compact approximations to Bayesian predictive distributions.

In*Twenty-second International Conference on Machine Learning***(ICML-2005)**. - Qi, Y, Minka, T.P., Picard, R.W., and Ghahramani, Z. (2004)

Predictive Automatic Relevance Determination by Expectation Propagation

In*Twenty-first International Conference on Machine Learning***(ICML-04)**. Banff, Alberta, Canada. - Minka, T.P., and Ghahramani, Z. (2003)

Expectation Propagation for Infinite Mixtures.

Technical Report, presented at the*NIPS 2003 Workshop on Nonparametric Bayesian Methods and Infinite Models*.

Talk and abstract at this website. - Kim, H.-C. and Ghahramani, Z. (2003)

The EM-EP Algorithm for Gaussian Process Classification

In the*Proceedings of the Workshop on Probabilistic Graphical Models for Classification (at ECML)*. Dubrovnik, Croatia. -
Beal, M. J. and Ghahramani, Z. (2002)

The Variational Bayesian EM Algorithm for Incomplete Data: with Application to Scoring Graphical Model Structures [pdf] [abstract]

In**Bayesian Statistics 7** - Ueda, N. and Ghahramani, Z. (2002)

Bayesian model search for mixture models based on optimizing variational bounds

**Neural Networks**15: 1223-1241. - Ghahramani, Z. and
Beal, M.J. (2001)

Propagation algorithms for variational Bayesian learning [pdf] [ps] [abstract]

In Leen, T.K., Dietterich, T.G., and Tresp, V. (eds)**Neural Information Processing Systems 13**:507-513. MIT Press. -
Ghahramani, Z. (2000)

Online Variational Bayesian Learning [pdf]

Slides from talk presented at NIPS 2000 workshop on Online Learning.

Joint work with H. Attias - Ghahramani, Z. and
Beal, M.J. (2000)

Graphical models and variational methods

In Saad & Opper (eds)**Advanced Mean Field Method---Theory and Practice.**MIT Press -
Ghahramani, Z. and Beal, M.J. (1999)

Variational inference for Bayesian mixtures of factor analysers [pdf] [ps] [abstract]

In**Neural Information Processing Systems 12** -
Jordan, M.I, Ghahramani, Z., Jaakkola, T.S., and Saul, L.K. (1999)

An introduction to variational methods for graphical models

**Machine Learning 37**:183-233. -
Ghahramani, Z. and Hinton, G.E. (1998)

Variational learning for switching state-space models

**Neural Computation**,**12**(4):963-996. [abstract] - Ghahramani, Z. (1997, revised 2002)

On Structured Variational Approximations

University of Toronto Technical Report CRG-TR-97-1, 6 pages (short note) - Ghahramani, Z. and Jordan, M.I. (1997)

Factorial Hidden Markov Models

**Machine Learning****29**: 245-273. [abstract]

Software written in Matlab. - Jordan, M.I, Ghahramani, Z. and Saul, L.K. (1997)

Hidden Markov Decision Trees

In*Advances in Neural Information Processing Systems 9,*7 pages. - Ghahramani, Z. (1995)

Factorial Learning and the EM Algorithm

In G. Tesauro, D.S. Touretzky, and J. Alspector (eds.),*Advances in Neural Information Processing Systems 7,*8 pages. [abstract]