# 2009 Research Summary

## Classification of Images with Hierarchical Beta Processes

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Romain Jean Thibaux, Michael Jordan and Erik Sudderth

The Indian buffet process [1] is a prior for binary vector observations. It is a nonparametric prior, allowing binary vectors of unbounded length. When representing data such as text as binary vectors--for instance each bit may represent the presence of a word--this prior gives Bayesian estimates of the probability of each bit. Used on texts of various categories or topics, a Naive Bayes classifier can be constructed based on these estimates.

A critical component of Naive Bayes is the smoothing and shrinking of parameters, through the sharing of statistical strengh between categories. Hierarchical beta processes [2] are an extension of Indian buffet processes that allow such sharing and outperform simpler smoothing methods. We now extend this work to categories of images, where obtaining a binary representation is less straightforward.

- [1]
- T. Griffiths and Z. Ghahramani, "Infinite Latent Feature Models and the Indian Buffet Process,"
*Advances in Neural Information Processing Systems (NIPS),*Vol. 18, 2005. - [2]
- R. Thibaux and M. I. Jordan, "Hierarchical Beta Processes and the Indian Buffet Process,"
*Eleventh International Conference on Artificial Intelligence and Statistics (AISTATS 2007),*San Juan, Puerto Rico, 2007.