IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/46-19.html
   My bibliography  Save this paper

Independent nonlinear component analysis

Author

Listed:
  • Florian Gunsilius

    (Institute for Fiscal Studies and MIT)

  • Susanne M. Schennach

    (Institute for Fiscal Studies and Brown University)

Abstract

The idea of summarizing the information contained in a large number of variables by a small number of “factors” or “principal components” has been broadly adopted in economics and statistics. This paper introduces a generalization of the widely used principal component analysis (PCA) to nonlinear settings, thus providing a new tool for dimension reduction and exploratory data analysis or representation. The distinguishing features of the method include (i) the ability to always deliver truly independent factors (as opposed to the merely uncorre-lated factors of PCA); (ii) the reliance on the theory of optimal transport and Brenier maps to obtain a robust and efficient computational algorithm; (iii) the use of a new multivariate additive entropy decomposition to determine the principal nonlinear components that capture most of the information content of the data and (iv) formally nesting PCA as a special case, for linear Gaussian factor models. We illustrate the method’s effectiveness in an application to the prediction of excess bond returns from a large number of macro factors.

Suggested Citation

  • Florian Gunsilius & Susanne M. Schennach, 2019. "Independent nonlinear component analysis," CeMMAP working papers CWP46/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:46/19
    as

    Download full text from publisher

    File URL: https://www.ifs.org.uk/uploads/CW4619-Independent-nonlinear-component-analysis.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers CWP58/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Kyle Jurado & Sydney C. Ludvigson & Serena Ng, 2015. "Measuring Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1177-1216, March.
    4. Susanne M. Schennach, 2014. "Entropic Latent Variable Integration via Simulation," Econometrica, Econometric Society, vol. 82(1), pages 345-385, January.
    5. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    6. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 560-586, June.
    7. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    8. Susan Athey & Guido W. Imbens, 2019. "Machine Learning Methods That Economists Should Know About," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 685-725, August.
    9. John H. Cochrane & Monika Piazzesi, 2005. "Bond Risk Premia," American Economic Review, American Economic Association, vol. 95(1), pages 138-160, March.
    10. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    11. Gregory, Allan W. & Head, Allen C., 1999. "Common and country-specific fluctuations in productivity, investment, and the current account," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 423-451, December.
    12. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
    13. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    14. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    15. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    16. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    17. Sydney C. Ludvigson & Serena Ng, 2009. "Macro Factors in Bond Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5027-5067, December.
    18. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers CWP58/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    20. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    21. Athey, Susan & Imbens, Guido W., 2019. "Machine Learning Methods Economists Should Know About," Research Papers 3776, Stanford University, Graduate School of Business.
    22. repec:hal:spmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    23. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    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. Hugo Freeman & Martin Weidner, 2021. "Linear Panel Regressions with Two-Way Unobserved Heterogeneity," Papers 2109.11911, arXiv.org, revised Aug 2022.
    2. Hugo Freeman & Martin Weidner, 2021. "Linear panel regressions with two-way unobserved heterogeneity," CeMMAP working papers CWP39/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Florian Gunsilius, 2020. "Distributional synthetic controls," Papers 2001.06118, arXiv.org, revised Dec 2021.

    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. Florian Gunsilius & Susanne M. Schennach, 2017. "A nonlinear principal component decomposition," CeMMAP working papers CWP16/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Dmitry Arkhangelsky, 2019. "Dealing with a Technological Bias: The Difference-in-Difference Approach," Working Papers wp2019_1903, CEMFI.
    3. Fan, Jianqing & Xue, Lingzhou & Yao, Jiawei, 2017. "Sufficient forecasting using factor models," Journal of Econometrics, Elsevier, vol. 201(2), pages 292-306.
    4. Li, Hongjun & Li, Qi & Shi, Yutang, 2017. "Determining the number of factors when the number of factors can increase with sample size," Journal of Econometrics, Elsevier, vol. 197(1), pages 76-86.
    5. repec:dau:papers:123456789/11663 is not listed on IDEAS
    6. Patrick Gagliardini & Elisa Ossola & Olivier Scaillet, 2016. "Time‐Varying Risk Premium in Large Cross‐Sectional Equity Data Sets," Econometrica, Econometric Society, vol. 84, pages 985-1046, May.
    7. repec:ipg:wpaper:19 is not listed on IDEAS
    8. Florian Gunsilius, 2018. "Point-identification in multivariate nonseparable triangular models," Papers 1806.09680, arXiv.org.
    9. Bouaddi, Mohammed & Taamouti, Abderrahim, 2013. "Portfolio selection in a data-rich environment," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2943-2962.
    10. Demetrescu, Matei & Hacıoğlu Hoke, Sinem, 2019. "Predictive regressions under asymmetric loss: Factor augmentation and model selection," International Journal of Forecasting, Elsevier, vol. 35(1), pages 80-99.
    11. Yannick Le Pen & Benoît Sévi, 2013. "Futures Trading and the Excess Comovement of Commodity Prices," Working Papers halshs-00793724, HAL.
    12. Mehmet Caner & Xu Han, 2014. "Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case With Group Bridge Estimators," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 359-374, July.
    13. Manuel Arellano & Stéphane Bonhomme, 2019. "Recovering Latent Variables by Matching," Working Papers wp2019_1914, CEMFI.
    14. repec:ipg:wpaper:2013-019 is not listed on IDEAS
    15. Simon Freyaldenhoven, 2020. "Identification Through Sparsity in Factor Models," Working Papers 20-25, Federal Reserve Bank of Philadelphia.
    16. Fan, Jianqing & Ke, Yuan & Liao, Yuan, 2021. "Augmented factor models with applications to validating market risk factors and forecasting bond risk premia," Journal of Econometrics, Elsevier, vol. 222(1), pages 269-294.
    17. Erdemlioglu, Deniz, 2009. "Macro Factors in UK Excess Bond Returns: Principal Components and Factor-Model Approach," MPRA Paper 28895, University Library of Munich, Germany.
    18. Marc Hallin, 2021. "Measure Transportation and Statistical Decision Theory," Working Papers ECARES 2021-04, ULB -- Universite Libre de Bruxelles.
    19. Buncic, Daniel & Tischhauser, Martin, 2017. "Macroeconomic factors and equity premium predictability," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 621-644.
    20. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2015. "Dynamic factor models with infinite-dimensional factor spaces: One-sided representations," Journal of Econometrics, Elsevier, vol. 185(2), pages 359-371.
    21. Soroosh Soofi-Siavash & Emanuel Moench, 2021. "What Moves Treasury Yields?," Bank of Lithuania Working Paper Series 88, Bank of Lithuania.
    22. Marc Hallin, 2018. "From Mahalanobis to Bregman via Monge and Kantorovich," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 135-146, December.
    23. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ifs:cemmap:46/19. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cmifsuk.html .

    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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.