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Variational Bayes estimation of hierarchical Dirichlet-multinomial mixtures for text clustering

Author

Listed:
  • Massimo Bilancia

    (University of Bari Aldo Moro, Policlinic University Hospital)

  • Michele Nanni

    (EY Business and Technology Solution)

  • Fabio Manca

    (University of Bari Aldo Moro, Palazzo Chiaia - Napolitano)

  • Gianvito Pio

    (University of Bari Aldo Moro)

Abstract

In this paper, we formulate a hierarchical Bayesian version of the Mixture of Unigrams model for text clustering and approach its posterior inference through variational inference. We compute the explicit expression of the variational objective function for our hierarchical model under a mean-field approximation. We then derive the update equations of a suitable algorithm based on coordinate ascent to find local maxima of the variational target, and estimate the model parameters through the optimized variational hyperparameters. The advantages of variational algorithms over traditional Markov Chain Monte Carlo methods based on iterative posterior sampling are also discussed in detail.

Suggested Citation

  • Massimo Bilancia & Michele Nanni & Fabio Manca & Gianvito Pio, 2023. "Variational Bayes estimation of hierarchical Dirichlet-multinomial mixtures for text clustering," Computational Statistics, Springer, vol. 38(4), pages 2015-2051, December.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:4:d:10.1007_s00180-023-01350-8
    DOI: 10.1007/s00180-023-01350-8
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    References listed on IDEAS

    as
    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. A. Pollice & M. Bilancia, 2000. "A hierarchical finite mixture model for Bayesian classification in the presence of auxiliary information," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 109-131.
    3. repec:dau:papers:123456789/3692 is not listed on IDEAS
    4. Zoubin Ghahramani, 2015. "Probabilistic machine learning and artificial intelligence," Nature, Nature, vol. 521(7553), pages 452-459, May.
    5. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    6. Laura Anderlucci & Cinzia Viroli, 2020. "Mixtures of Dirichlet-Multinomial distributions for supervised and unsupervised classification of short text data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(4), pages 759-770, December.
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    Cited by:

    1. Massimo Bilancia & Andrea Nigri & Samuele Magro, 2025. "Stochastic variational inference for clustering short text data with finite mixtures of Dirichlet-Multinomial distributions," Statistical Papers, Springer, vol. 66(4), pages 1-39, June.

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