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Topic Models - LDA and Correlated Topic Models

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Claudia Wagner
Claudia Wagner

Seminar Talk at Computational Intelligence Seminar F, Technical University Graz

Tecnología
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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
  • 4.
  • 5. Latent Dirichlet Allocation (LDA) (Blei et al, 2003)
  • 6.
  • 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.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16. Correlated Topic Models (CTM) (Blei et al, 2007)
  • 17.
  • 18.
  • 19.
  • 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.
  • 22.
  • 23.
  • 24. Empirical Results Comparing CTM and LDA (Blei et al, 2007)
  • 25.
  • 26.
  • 27.
  • 28.