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Latent Dirichlet Allocation

Written for the Research library (claude-opus-5-5) from the paper text, in our own words: the license "JMLR — open access, read only" does not allow redistributing the text itself. Original — jmlr.org/papers/volume3/blei03a/blei03a.pdf

Summary

The paper addresses how to obtain compact, statistically meaningful representations of documents and other collections of discrete data. Earlier approaches fall short in different ways. tf-idf and LSI compress data but reveal little probabilistic structure. Hofmann's pLSI has no generative model at the document level, so its parameter count grows with the corpus, it overfits, and it cannot naturally score unseen documents. Starting from de Finetti's theorem on exchangeable variables, the authors propose latent Dirichlet allocation (LDA), a three-level hierarchical Bayesian model. In LDA, each document draws a topic mixture from a Dirichlet prior, and every word is produced by first sampling a topic and then a word from that topic's distribution. Exact inference is intractable, so they derive a variational approximation and an EM procedure for empirical Bayes parameter estimation. Experiments cover document modeling, text classification and collaborative filtering, with mixture of unigrams and pLSI as baselines. In the collaborative filtering experiment, LDA gives the best predictive perplexity, even though both baselines receive overfitting corrections. Because LDA is modular and extensible, it can serve as a building block for richer probabilistic models.

Key points

  • Generative process: document length N is drawn from a Poisson distribution, topic proportions θ from Dir(α), and each word comes from a topic-specific multinomial. Word probabilities form a k×V matrix β, with the number of topics k fixed in advance.
  • Baselines are the mixture of unigrams model and pLSI (the aspect model). A key criticism of pLSI is that its parameters scale linearly with corpus size.
  • The collaborative filtering setup uses EachMovie, keeping only users with at least 100 positive ratings (4 or more of 5 stars). This yields 3300 training and 390 test users and a vocabulary of 1600 movies, evaluated by predictive perplexity on a held-out movie.
  • Inference relies on a convexity-based variational method. The authors point to expectation propagation (Minka and Lafferty) and MCMC (Griffiths and Steyvers) as alternative inference approaches.
  • Proposed extensions include Gaussian or other non-multinomial emissions, mixtures of Dirichlets, time-series topics, and conditioning on paragraph or sentence features. Paired LDA modules have already been used to model images with their captions.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

Fields: Computing & GPUs

Cited by

1948 papers of our library cite it (of the 140673 whose bibliographies we read); 31 of them have a page here, 1917 not yet.

Cite

The paper itself, not this page. BibTeX from the library's record of the work.

@inproceedings{blei2003latent,
  title = {{Latent Dirichlet Allocation}},
  author = {Blei, David M. and Ng, Andrew Y. and Jordan, Michael I.},
  booktitle = {JMLR 3},
  year = {2003}
}

References

13 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

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