IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v64y2012i5p1009-1044.html
   My bibliography  Save this article

Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation

Author

Listed:
  • Masashi Sugiyama
  • Taiji Suzuki
  • Takafumi Kanamori

Abstract

Estimation of the ratio of probability densities has attracted a great deal of attention since it can be used for addressing various statistical paradigms. A naive approach to density-ratio approximation is to first estimate numerator and denominator densities separately and then take their ratio. However, this two-step approach does not perform well in practice, and methods for directly estimating density ratios without density estimation have been explored. In this paper, we first give a comprehensive review of existing density-ratio estimation methods and discuss their pros and cons. Then we propose a new framework of density-ratio estimation in which a density-ratio model is fitted to the true density-ratio under the Bregman divergence. Our new framework includes existing approaches as special cases, and is substantially more general. Finally, we develop a robust density-ratio estimation method under the power divergence, which is a novel instance in our framework. Copyright The Institute of Statistical Mathematics, Tokyo 2012

Suggested Citation

  • Masashi Sugiyama & Taiji Suzuki & Takafumi Kanamori, 2012. "Density-ratio matching under the Bregman divergence: a unified framework of density-ratio estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1009-1044, October.
    • Handle: RePEc:spr:aistmt:v:64:y:2012:i:5:p:1009-1044
    DOI: 10.1007/s10463-011-0343-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-011-0343-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-011-0343-8?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. Masashi Sugiyama & Taiji Suzuki & Shinichi Nakajima & Hisashi Kashima & Paul Bünau & Motoaki Kawanabe, 2008. "Direct importance estimation for covariate shift adaptation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 699-746, December.
    2. Sugiyama Masashi & Müller Klaus-Robert, 2005. "Input-dependent estimation of generalization error under covariate shift," Statistics & Risk Modeling, De Gruyter, vol. 23(4), pages 249-279, April.
    3. B. W. Silverman, 1978. "Density Ratios, Empirical Likelihood and Cot Death," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(1), pages 26-33, March.
    4. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    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. Gaëlle Chagny & Claire Lacour, 2015. "Optimal adaptive estimation of the relative density," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 605-631, September.
    2. Yukitoshi Matsushita & Taisuke Otsu & Keisuke Takahata, 2022. "Estimating density ratio of marginals to joint: Applications to causal inference," STICERD - Econometrics Paper Series 619, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Abdolnasser Sadeghkhani & Yingwei Peng & Chunfang Devon Lin, 2019. "A Parametric Bayesian Approach in Density Ratio Estimation," Stats, MDPI, vol. 2(2), pages 1-13, March.
    4. David Bruns-Smith & Oliver Dukes & Avi Feller & Elizabeth L. Ogburn, 2023. "Augmented balancing weights as linear regression," Papers 2304.14545, arXiv.org, revised Jun 2024.

    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. Arun Kumar Kuchibhotla & Somabha Mukherjee & Ayanendranath Basu, 2019. "Statistical inference based on bridge divergences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 627-656, June.
    2. Sheng, Haiyang & Yu, Guan, 2023. "TNN: A transfer learning classifier based on weighted nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    3. Abhijit Mandal & Beste Hamiye Beyaztas & Soutir Bandyopadhyay, 2023. "Robust density power divergence estimates for panel data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 773-798, October.
    4. Jiaming Mao & Jingzhi Xu, 2020. "Ensemble Learning with Statistical and Structural Models," Papers 2006.05308, arXiv.org.
    5. Hirose, Kei & Fujisawa, Hironori & Sese, Jun, 2017. "Robust sparse Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 172-190.
    6. Gaëlle Chagny & Claire Lacour, 2015. "Optimal adaptive estimation of the relative density," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 605-631, September.
    7. Dylan Brewer & Alyssa Carlson, 2024. "Addressing sample selection bias for machine learning methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(3), pages 383-400, April.
    8. Masashi Sugiyama & Taiji Suzuki & Shinichi Nakajima & Hisashi Kashima & Paul Bünau & Motoaki Kawanabe, 2008. "Direct importance estimation for covariate shift adaptation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 699-746, December.
    9. Shogo Kato & Shinto Eguchi, 2016. "Robust estimation of location and concentration parameters for the von Mises–Fisher distribution," Statistical Papers, Springer, vol. 57(1), pages 205-234, March.
    10. Takayuki Kawashima & Hironori Fujisawa, 2023. "Robust regression against heavy heterogeneous contamination," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(4), pages 421-442, May.
    11. Nishiyama, Tomohiro, 2019. "A New Lower Bound for Kullback-Leibler Divergence Based on Hammersley-Chapman-Robbins Bound," OSF Preprints wa98j, Center for Open Science.
    12. Chen, Ting-Li & Fujisawa, Hironori & Huang, Su-Yun & Hwang, Chii-Ruey, 2016. "On the weak convergence and Central Limit Theorem of blurring and nonblurring processes with application to robust location estimation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 165-184.
    13. Mingyang Ren & Sanguo Zhang & Qingzhao Zhang, 2021. "Robust high-dimensional regression for data with anomalous responses," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 703-736, August.
    14. Yannis Yatracos, 2013. "Equal percent bias reduction and variance proportionate modifying properties with mean–covariance preserving matching," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 69-87, February.
    15. Byol Kim & Song Liu & Mladen Kolar, 2021. "Two‐sample inference for high‐dimensional Markov networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 939-962, November.
    16. Masahiro Kato & Hikaru Kawarazaki, 2019. "Model Specification Test with Unlabeled Data: Approach from Covariate Shift," Papers 1911.00688, arXiv.org, revised Feb 2020.
    17. Gayen, Atin & Kumar, M. Ashok, 2021. "Projection theorems and estimating equations for power-law models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    18. Zhexiao Lin & Peng Ding & Fang Han, 2023. "Estimation Based on Nearest Neighbor Matching: From Density Ratio to Average Treatment Effect," Econometrica, Econometric Society, vol. 91(6), pages 2187-2217, November.
    19. Yukitoshi Matsushita & Taisuke Otsu & Keisuke Takahata, 2022. "Estimating density ratio of marginals to joint: Applications to causal inference," STICERD - Econometrics Paper Series 619, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    20. Abdolnasser Sadeghkhani & Yingwei Peng & Chunfang Devon Lin, 2019. "A Parametric Bayesian Approach in Density Ratio Estimation," Stats, MDPI, vol. 2(2), pages 1-13, March.

    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:aistmt:v:64:y:2012:i:5:p:1009-1044. 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.