Regularized nonlinear regression for simultaneously selecting and estimating key model parameters: Application to head-neck position tracking

Kyubaek Yoon, Hojun You, Wei Ying Wu, Chae Young Lim, Jongeun Choi, Connor Boss, Ahmed Ramadan, John M. Popovich, Jacek Cholewicki, N. Peter Reeves, Clark J. Radcliffe

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In system identification, estimating parameters of a biomechanical model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model parameters while fixing the remaining parameters to a set of typical values. The problem is formulated as a nonlinear least-squares estimator with L1-regularization on the deviation of parameters from a set of typical values. In addition, a modified optimization approach is introduced to find the solution to the formulated problem. As a result, we provided consistency and oracle properties of the proposed estimator as a theoretical foundation. To show the effectiveness of the proposed method, we conducted simulation and experimental studies. In the simulation study, the proposed Lasso performed significantly better than the ordinary L1-regularization methods in terms of the bias and variance of the parameter estimates. The experimental study presented an application identifying a biomechanical parametric model of a head position tracking task for ten human subjects from limited data. Compared with the variance of the parameter estimates from nonlinear ordinary least-squares regression, that of parameter estimates from the proposed Lasso decreased by 96% using the simulated data. Using the real-world data, the variance of estimated parameters decreased by 71%. In addition, the proposed method kept variance accounted for (VAF) at 83% and was 54 times faster than the ordinary Lasso using a standard simplex-based optimization algorithm.

Original languageEnglish
Article number104974
JournalEngineering Applications of Artificial Intelligence
Publication statusPublished - 2022 Aug

Bibliographical note

Funding Information:
This work was supported by the Mid-career Research Programs and Basic Research Laboratory through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT ( NRF-2019R1A2C1002213 , 2020R1A4A1018207 , 2021R1A2B5B01002620 ). This work was supported by Yonsei-KIST Convergence Research Program . This publication was made possible by grant number U19AT006057 from the National Center for Complementary and Integrative Health (NCCIH) at the National Institutes of Health. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of NCCIH. The research of Wei-Ying Wu was supported by Ministry of Science and Technology of Taiwan under grants ( MOST 108-2118-M-259-002-MY2 ).

Publisher Copyright:
© 2022 Elsevier Ltd

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering


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