IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921011085.html
   My bibliography  Save this article

An efficient primal-dual method for solving non-smooth machine learning problem

Author

Listed:
  • Lyaqini, S.
  • Nachaoui, M.
  • Hadri, A.

Abstract

This paper deals with the machine learning model as a framework of regularized loss minimization problem in order to obtain a generalized model. Recently, some studies have proved the success and the efficiency of nonsmooth loss function for supervised learning problems Lyaqini et al. [1]. Motivated by the success of this choice, in this paper we formulate the supervised learning problem based on L1 fidelity term. To solve this nonsmooth optimization problem we transform it into a mini-max one. Then we propose a Primal-Dual method that handles the mini-max problem. This method leads to an efficient and significantly faster numerical algorithm to solve supervised learning problems in the most general case. To illustrate the effectiveness of the proposed approach we present some experimental-numerical validation examples, which are made through synthetic and real-life data. Thus, we show that our approach is outclassing existing methods in terms of convergence speed, quality, and stability of the predicted models.

Suggested Citation

  • Lyaqini, S. & Nachaoui, M. & Hadri, A., 2022. "An efficient primal-dual method for solving non-smooth machine learning problem," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921011085
    DOI: 10.1016/j.chaos.2021.111754
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921011085
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111754?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. Mee Young Park & Trevor Hastie, 2007. "L1‐regularization path algorithm for generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 659-677, September.
    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    3. Adi L Tarca & Vincent J Carey & Xue-wen Chen & Roberto Romero & Sorin Drăghici, 2007. "Machine Learning and Its Applications to Biology," PLOS Computational Biology, Public Library of Science, vol. 3(6), pages 1-11, June.
    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. Dumitrescu, Elena & Hué, Sullivan & Hurlin, Christophe & Tokpavi, Sessi, 2022. "Machine learning for credit scoring: Improving logistic regression with non-linear decision-tree effects," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1178-1192.
    2. Elena Ivona DUMITRESCU & Sullivan HUE & Christophe HURLIN & Sessi TOKPAVI, 2020. "Machine Learning or Econometrics for Credit Scoring: Let’s Get the Best of Both Worlds," LEO Working Papers / DR LEO 2839, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    3. Dai, Wei & Tsang, Ka Wai, 2023. "A resampling approach for confidence intervals in linear time-series models after model selection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    4. Jian Huang & Yuling Jiao & Lican Kang & Jin Liu & Yanyan Liu & Xiliang Lu, 2022. "GSDAR: a fast Newton algorithm for $$\ell _0$$ ℓ 0 regularized generalized linear models with statistical guarantee," Computational Statistics, Springer, vol. 37(1), pages 507-533, March.
    5. Laura Ciarloni & Sahar Hosseinian & Sylvain Monnier-Benoit & Natsuko Imaizumi & Gian Dorta & Curzio Ruegg & On behalf of the DGNP-COL-0310 Study Group, 2015. "Discovery of a 29-Gene Panel in Peripheral Blood Mononuclear Cells for the Detection of Colorectal Cancer and Adenomas Using High Throughput Real-Time PCR," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-17, April.
    6. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    7. Ernesto Carrella & Richard M. Bailey & Jens Koed Madsen, 2018. "Indirect inference through prediction," Papers 1807.01579, arXiv.org.
    8. Rui Wang & Naihua Xiu & Kim-Chuan Toh, 2021. "Subspace quadratic regularization method for group sparse multinomial logistic regression," Computational Optimization and Applications, Springer, vol. 79(3), pages 531-559, July.
    9. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    10. Masakazu Higuchi & Mitsuteru Nakamura & Shuji Shinohara & Yasuhiro Omiya & Takeshi Takano & Daisuke Mizuguchi & Noriaki Sonota & Hiroyuki Toda & Taku Saito & Mirai So & Eiji Takayama & Hiroo Terashi &, 2022. "Detection of Major Depressive Disorder Based on a Combination of Voice Features: An Exploratory Approach," IJERPH, MDPI, vol. 19(18), pages 1-13, September.
    11. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    12. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    13. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
    14. Perrot-Dockès Marie & Lévy-Leduc Céline & Chiquet Julien & Sansonnet Laure & Brégère Margaux & Étienne Marie-Pierre & Robin Stéphane & Genta-Jouve Grégory, 2018. "A variable selection approach in the multivariate linear model: an application to LC-MS metabolomics data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 17(5), pages 1-14, October.
    15. Fan, Jianqing & Jiang, Bai & Sun, Qiang, 2022. "Bayesian factor-adjusted sparse regression," Journal of Econometrics, Elsevier, vol. 230(1), pages 3-19.
    16. Jun Li & Serguei Netessine & Sergei Koulayev, 2018. "Price to Compete … with Many: How to Identify Price Competition in High-Dimensional Space," Management Science, INFORMS, vol. 64(9), pages 4118-4136, September.
    17. Sung Jae Jun & Sokbae Lee, 2020. "Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions," Papers 2004.08318, arXiv.org, revised Oct 2023.
    18. Rina Friedberg & Julie Tibshirani & Susan Athey & Stefan Wager, 2018. "Local Linear Forests," Papers 1807.11408, arXiv.org, revised Sep 2020.
    19. Xiangwei Li & Thomas Delerue & Ben Schöttker & Bernd Holleczek & Eva Grill & Annette Peters & Melanie Waldenberger & Barbara Thorand & Hermann Brenner, 2022. "Derivation and validation of an epigenetic frailty risk score in population-based cohorts of older adults," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    20. Hewamalage, Hansika & Bergmeir, Christoph & Bandara, Kasun, 2021. "Recurrent Neural Networks for Time Series Forecasting: Current status and future directions," International Journal of Forecasting, Elsevier, vol. 37(1), pages 388-427.

    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:eee:chsofr:v:155:y:2022:i:c:s0960077921011085. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.