• Corpus ID: 17798922

# Probable convexity and its application to Correlated Topic Models

@article{Than2013ProbableCA,
title={Probable convexity and its application to Correlated Topic Models},
author={Khoat Than and Tu Bao Ho},
journal={ArXiv},
year={2013},
volume={abs/1312.4527}
}
• Published 16 December 2013
• Computer Science
• ArXiv
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In this work, we attack non-convexity by first introducing the concept of \emph{probable convexity} for analyzing convexity of real functions in practice. We then use the new concept to analyze an inference problem in the \emph{Correlated Topic Model} (CTM) and…

## References

SHOWING 1-10 OF 26 REFERENCES

• Computer Science
NIPS
• 2011
This work studies the problem of finding the maximum a posteriori (MAP) assignment of topics to words, where the document's topic distribution is integrated out, and shows that, when the effective number of topics per document is small, exact inference takes polynomial time, and that this problem is NP-hard.
• Computer Science
• 2007
The correlated topic model (CTM) is developed, where the topic proportions exhibit correlation via the logistic normal distribution, and it is demonstrated its use as an exploratory tool of large document collections.
• Computer Science
SDM
• 2009
A new extension of the CTM method to enable modeling with multi-field topics in a global graphical structure, and a mean-field variational algorithm to allow joint learning of multinomial topic models from discrete data and Gaussianstyle topic models for real-valued data are proposed.
• Computer Science
ECML/PKDD
• 2012
This paper shows that FSTM can perform substantially better than various existing topic models by different performance measures, and provides a principled way to directly trade off sparsity of solutions against inference quality and running time.
• Computer Science
ICML
• 2012
This work presents efficient online learning algorithms that eschew projections in favor of much more efficient linear optimization steps using the Frank-Wolfe technique, and obtains a range of regret bounds for online convex optimization, with better bounds for specific cases such as stochastic online smooth conveX optimization.
• Computer Science
IEEE Transactions on Automatic Control
• 2006
A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.
• Computer Science
J. Mach. Learn. Res.
• 2010
An alternative to the Dirichlet prior is suggested, a family of logistic normal distributions that permits soft parameter tying within grammars and across Grammars for text in different languages, and empirical gains in a novel learning setting using bilingual, non-parallel data are shown.
• Computer Science
EMNLP
• 2011
A novel statistical topic model based on an automated evaluation metric based on this metric that significantly improves topic quality in a large-scale document collection from the National Institutes of Health (NIH).
• Mathematics, Computer Science
Theory Comput.
• 2008
This work derandomizes an efficient construction by Alon and Roichman of an expanding Cayley graph of logarithmic degree on any (possibly non-abelian) group and applies these pessimistic estimators to the problem of solving semidefinite covering problems, giving a deterministic algorithm for the quantum hypergraph cover problem of Ahslwede and Winter.
• Computer Science
2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
• 2010
The proposed association model shows improved performance over correspondence LDA as measured by caption perplexity, and a novel latent variable regression approach to capture correlations between image or video features and annotation texts.