IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i11p1682-d1403981.html
   My bibliography  Save this article

Entry-Wise Eigenvector Analysis and Improved Rates for Topic Modeling on Short Documents

Author

Listed:
  • Zheng Tracy Ke

    (Department of Statistics, Harvard University, Cambridge, MA 02138, USA)

  • Jingming Wang

    (Department of Statistics, Harvard University, Cambridge, MA 02138, USA)

Abstract

Topic modeling is a widely utilized tool in text analysis. We investigate the optimal rate for estimating a topic model. Specifically, we consider a scenario with n documents, a vocabulary of size p , and document lengths at the order N . When N ≥ c · p , referred to as the long-document case, the optimal rate is established in the literature at p / ( N n ) . However, when N = o ( p ) , referred to as the short-document case, the optimal rate remains unknown. In this paper, we first provide new entry-wise large-deviation bounds for the empirical singular vectors of a topic model. We then apply these bounds to improve the error rate of a spectral algorithm, Topic-SCORE. Finally, by comparing the improved error rate with the minimax lower bound, we conclude that the optimal rate is still p / ( N n ) in the short-document case.

Suggested Citation

  • Zheng Tracy Ke & Jingming Wang, 2024. "Entry-Wise Eigenvector Analysis and Improved Rates for Topic Modeling on Short Documents," Mathematics, MDPI, vol. 12(11), pages 1-41, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1682-:d:1403981
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/11/1682/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/11/1682/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ruijia Wu & Linjun Zhang & T. Tony Cai, 2023. "Sparse Topic Modeling: Computational Efficiency, Near-Optimal Algorithms, and Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1849-1861, July.
    2. Zheng Tracy Ke & Minzhe Wang, 2024. "Using SVD for Topic Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 434-449, January.
    3. Jianqing Fan & Yingying Fan & Xiao Han & Jinchi Lv, 2022. "SIMPLE: Statistical inference on membership profiles in large networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 630-653, April.
    Full references (including those not matched with items on IDEAS)

    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. Jin, Jiashun & Ke, Zheng Tracy & Luo, Shengming, 2024. "Mixed membership estimation for social networks," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Laura Battaglia & Timothy M. Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for regression with variables generated from unstructured data," CeMMAP working papers 10/24, Institute for Fiscal Studies.
    3. Laura Battaglia & Timothy Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for Regression with Variables Generated by AI or Machine Learning," Papers 2402.15585, arXiv.org, revised Dec 2024.

    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:gam:jmathe:v:12:y:2024:i:11:p:1682-:d:1403981. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.