IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v38y2023i4d10.1007_s00180-023-01350-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-023-01350-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-023-01350-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuan Fang & Dimitris Karlis & Sanjeena Subedi, 2022. "Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 510-552, November.
    2. O’Dwyer, Edward & Pan, Indranil & Acha, Salvador & Shah, Nilay, 2019. "Smart energy systems for sustainable smart cities: Current developments, trends and future directions," Applied Energy, Elsevier, vol. 237(C), pages 581-597.
    3. 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.
    4. Riccardo Rastelli & Michael Fop, 2020. "A stochastic block model for interaction lengths," 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(2), pages 485-512, June.
    5. Diana Mindrila, 2023. "Bayesian Latent Class Analysis: Sample Size, Model Size, and Classification Precision," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    6. Zhang, Jincheng & Zhao, Xiaowei & Jin, Siya & Greaves, Deborah, 2022. "Phase-resolved real-time ocean wave prediction with quantified uncertainty based on variational Bayesian machine learning," Applied Energy, Elsevier, vol. 324(C).
    7. Gao Wang & Abhishek Sarkar & Peter Carbonetto & Matthew Stephens, 2020. "A simple new approach to variable selection in regression, with application to genetic fine mapping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1273-1300, December.
    8. Zaid Tashman & Christoph Gorder & Sonali Parthasarathy & Mohamad M. Nasr-Azadani & Rachel Webre, 2020. "Anomaly Detection System for Water Networks in Northern Ethiopia Using Bayesian Inference," Sustainability, MDPI, vol. 12(7), pages 1-16, April.
    9. Angela Maria D’Uggento & Albino Biafora & Fabio Manca & Claudia Marin & Massimo Bilancia, 2023. "A text data mining approach to the study of emotions triggered by new advertising formats during the COVID-19 pandemic," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(3), pages 2303-2325, June.
    10. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "State Space Approach to Adaptive Artificial Intelligence Modeling: Application to Financial Portfolio with Fuzzy System," CARF F-Series CARF-F-422, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    12. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    13. Arman Oganisian & Nandita Mitra & Jason A. Roy, 2021. "A Bayesian nonparametric model for zero‐inflated outcomes: Prediction, clustering, and causal estimation," Biometrics, The International Biometric Society, vol. 77(1), pages 125-135, March.
    14. Shen Liu & Hongyan Liu, 2021. "Tagging Items Automatically Based on Both Content Information and Browsing Behaviors," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 882-897, July.
    15. Wilson, Christopher & van der Velden, Maja, 2022. "Sustainable AI: An integrated model to guide public sector decision-making," Technology in Society, Elsevier, vol. 68(C).
    16. repec:ags:aaea22:335590 is not listed on IDEAS
    17. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    18. Rufo, M.J. & Pérez, C.J. & Martín, J., 2009. "Local parametric sensitivity for mixture models of lifetime distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1238-1244.
    19. Li, Yi & Liu, Kailong & Foley, Aoife M. & Zülke, Alana & Berecibar, Maitane & Nanini-Maury, Elise & Van Mierlo, Joeri & Hoster, Harry E., 2019. "Data-driven health estimation and lifetime prediction of lithium-ion batteries: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 113(C), pages 1-1.
    20. Jeong Eun Lee & Christian Robert, 2013. "Imortance Sampling Schemes for Evidence Approximation in Mixture Models," Working Papers 2013-42, Center for Research in Economics and Statistics.
    21. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:38:y:2023:i:4:d:10.1007_s00180-023-01350-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.