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Computational Intelligence Seminar F  Topic Models LDA and the Correlated Topic Models Claudia Wagner Graz, 21.1.2011
Motivation ,[object Object],[object Object],[object Object],[object Object]
  Topic Models Generative Models http://www.cs.umass.edu/~wallach/talks/priors.pdf
Topic Models Statistical Inference ,[object Object],[object Object],[object Object],[object Object],θ (d ) φ (z) z i http://videolectures.net/mlss09uk_blei_tm/ ,[object Object],[object Object],[object Object],[object Object]
Latent Dirichlet Allocation (LDA)   (Blei et al, 2003)
LDA ,[object Object],[object Object],[object Object],[object Object],P( w | z,  φ  (z)   ) number of documents number of words
Matrix Representation  of LDA observed latent latent θ φ
Dirichlet Distribution
Dirichlet Distribution The larger the value of the concentration parameter alpha, the more evenly distributed is the resulting distribution!  Low  α Topic1 Topic 2 Topic 3 Examples with K=3 http://www.cs.umass.edu/~wallach/talks/priors.pdf θ i  = (1, 0, 0) High  α High  α θ i  = (1/3, 1/3, 1/3) More smoothing Less smoothing Topic1 Topic 2 Topic 3 ?
Dirichlet Priors  α and  β ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Posterior Distribution of LDA  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
(Collapsed) Gibbs Sampling ,[object Object],[object Object],[object Object],[object Object]
Collapsed Gibbs Sampling ,[object Object],[object Object],[object Object],[object Object],[object Object],Topic counts Current state of  hidden vars Observation How likely is the word wi for topic t? How likely is topic t?
Variational Methods ,[object Object],[object Object],[object Object],[object Object]
Why does LDA work?  ,[object Object],[object Object],[object Object],[object Object],[object Object]
Correlated Topic Models (CTM)   (Blei et al, 2007)
CTM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
CTM ,[object Object],covariance matrix  K x K topic distribution  per document word distribution  per per topic K dimensional  positive vector
Logistic normal distribution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Dirichlet versus  L ogistic Normal http://www.cs.princeton.edu/~blei/modeling-science.pdf Dirichlet distribution (Paramter: postive K-dim vector α) Logistic Normal distribution (Paramter: postive K-dim vector  μ ,  K x K co-variance Matrix  Ʃ ) High  α Low  α High  α unsymmetric symmetric symmetric diagonal covariance  negative correlation  between topics 1 and 2  positive correlation  between topics 1 and 2  Topic1 Topic2 Topic3
Posterior of  CTM ,[object Object],[object Object],[object Object],[object Object],N … Num of words K … Num of topics
Approximate Posterior of  CTM ,[object Object],[object Object],[object Object],[object Object]
Gibbs Sampling ,[object Object],[object Object],How likely is the word wi for topic t? How likely is topic t for this document?
Empirical Results  Comparing CTM and LDA   (Blei et al, 2007)
Experimental Setup ,[object Object],[object Object],[object Object],[object Object],[object Object],Num of words  per document Num of  observed words
Results ,[object Object],[object Object]
Results ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
References ,[object Object],[object Object],[object Object]

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Topic Models - LDA and Correlated Topic Models

  • 1. Computational Intelligence Seminar F Topic Models LDA and the Correlated Topic Models Claudia Wagner Graz, 21.1.2011
  • 2.
  • 3. Topic Models Generative Models http://www.cs.umass.edu/~wallach/talks/priors.pdf
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  • 5. Latent Dirichlet Allocation (LDA) (Blei et al, 2003)
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  • 7. Matrix Representation of LDA observed latent latent θ φ
  • 9. Dirichlet Distribution The larger the value of the concentration parameter alpha, the more evenly distributed is the resulting distribution! Low α Topic1 Topic 2 Topic 3 Examples with K=3 http://www.cs.umass.edu/~wallach/talks/priors.pdf θ i = (1, 0, 0) High α High α θ i = (1/3, 1/3, 1/3) More smoothing Less smoothing Topic1 Topic 2 Topic 3 ?
  • 10.
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  • 16. Correlated Topic Models (CTM) (Blei et al, 2007)
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  • 20. Dirichlet versus L ogistic Normal http://www.cs.princeton.edu/~blei/modeling-science.pdf Dirichlet distribution (Paramter: postive K-dim vector α) Logistic Normal distribution (Paramter: postive K-dim vector μ , K x K co-variance Matrix Ʃ ) High α Low α High α unsymmetric symmetric symmetric diagonal covariance negative correlation between topics 1 and 2 positive correlation between topics 1 and 2 Topic1 Topic2 Topic3
  • 21.
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  • 23.
  • 24. Empirical Results Comparing CTM and LDA (Blei et al, 2007)
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  • 28.