IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v182y2024ics0960077924002856.html
   My bibliography  Save this article

Sparse least squares via fractional function group fractional function penalty for the identification of nonlinear dynamical systems

Author

Listed:
  • Lu, Yisha
  • Hu, Yaozhong
  • Qiao, Yan
  • Yuan, Minjuan
  • Xu, Wei

Abstract

This work proposes a method called fractional function group fractional function penalty sparse least squares to identify nonlinear dynamical systems. It integrates least squares with fractional function group fractional function penalty with the aim to enhance sparsity and accuracy of regression tasks. Additionally, we develop an optimization algorithm called the threshold fractional function group fractional function penalty sparse least squares. The choice of threshold parameters throughout the algorithm is accomplished by employing the L-curve criterion. The simulation experiments involving two ordinary differential equations and one partial differential equation illustrate that our proposed method has superior identification performance especially on larger noisy state measurements compared to existing methods, signifying that our new method is effective across a wide variety of latent applications.

Suggested Citation

  • Lu, Yisha & Hu, Yaozhong & Qiao, Yan & Yuan, Minjuan & Xu, Wei, 2024. "Sparse least squares via fractional function group fractional function penalty for the identification of nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924002856
    DOI: 10.1016/j.chaos.2024.114733
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924002856
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114733?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. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Friedman, Jerome H., 2012. "Fast sparse regression and classification," International Journal of Forecasting, Elsevier, vol. 28(3), pages 722-738.
    3. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    4. Xiaotong Shen & Wei Pan & Yunzhang Zhu, 2012. "Likelihood-Based Selection and Sharp Parameter Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 223-232, March.
    5. G. M. Fung & O. L. Mangasarian, 2011. "Equivalence of Minimal ℓ 0- and ℓ p -Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 1-10, October.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    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. 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.
    2. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.
    3. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    4. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    5. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    6. Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    7. Hu, Jianhua & Liu, Xiaoqian & Liu, Xu & Xia, Ningning, 2022. "Some aspects of response variable selection and estimation in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    9. Guo, Xiao & Zhang, Hai & Wang, Yao & Wu, Jiang-Lun, 2015. "Model selection and estimation in high dimensional regression models with group SCAD," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 86-92.
    10. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    11. Kwon, Sunghoon & Oh, Seungyoung & Lee, Youngjo, 2016. "The use of random-effect models for high-dimensional variable selection problems," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 401-412.
    12. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso," Journal of Econometrics, Elsevier, vol. 191(1), pages 86-109.
    13. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    14. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
    15. Behrendt, Simon & Schweikert, Karsten, 2021. "A Note on Adaptive Group Lasso for Structural Break Time Series," Econometrics and Statistics, Elsevier, vol. 17(C), pages 156-172.
    16. Yanhang Zhang & Junxian Zhu & Jin Zhu & Xueqin Wang, 2023. "A Splicing Approach to Best Subset of Groups Selection," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 104-119, January.
    17. Zhihua Sun & Yi Liu & Kani Chen & Gang Li, 2022. "Broken adaptive ridge regression for right-censored survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 69-91, February.
    18. Gerhard Tutz & Margret-Ruth Oelker, 2017. "Modelling Clustered Heterogeneity: Fixed Effects, Random Effects and Mixtures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 204-227, August.
    19. Shanshan Qin & Hao Ding & Yuehua Wu & Feng Liu, 2021. "High-dimensional sign-constrained feature selection and grouping," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 787-819, August.
    20. Kaida Cai & Hua Shen & Xuewen Lu, 2022. "Adaptive bi-level variable selection for multivariate failure time model with a diverging number of covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 968-993, December.

    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:182:y:2024:i:c:s0960077924002856. 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.