A Stick-Breaking Likelihood for Categorical Data Analysis with Latent Gaussian Models
Abstract
The development of accurate models and efficient algorithms for the analysis of multivariate categorical data are important and long-standing problems in machine learning and computational statistics. In this paper, we focus on modeling categorical data using Latent Gaussian Models (LGMs). We propose a novel stick-breaking likelihood function for categorical LGMs that exploits accurate linear and quadratic bounds on the logistic log-partition function, leading to an effective variational inference and learning framework. We thoroughly compare our approach to existing algorithms for multinomial logit/probit likelihoods on several problems, including inference in multinomial Gaussian process classification and learning in latent factor models. Our extensive comparisons demonstrate that our stick-breaking model effectively captures correlation in discrete data and is well suited for the analysis of categorical data.
Cite
Text
Khan et al. "A Stick-Breaking Likelihood for Categorical Data Analysis with Latent Gaussian Models." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.Markdown
[Khan et al. "A Stick-Breaking Likelihood for Categorical Data Analysis with Latent Gaussian Models." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.](https://mlanthology.org/aistats/2012/khan2012aistats-stickbreaking/)BibTeX
@inproceedings{khan2012aistats-stickbreaking,
title = {{A Stick-Breaking Likelihood for Categorical Data Analysis with Latent Gaussian Models}},
author = {Khan, Mohammad and Mohamed, Shakir and Marlin, Benjamin and Murphy, Kevin},
booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics},
year = {2012},
pages = {610-618},
volume = {22},
url = {https://mlanthology.org/aistats/2012/khan2012aistats-stickbreaking/}
}