Regularized Nonlinear Regression for Simultaneously Selecting and Estimating Key Model Parameters

• URL: http://arxiv.org/abs/2104.11426v1
• Date: Fri, 23 Apr 2021 06:17:57 GMT
• Title: Regularized Nonlinear Regression for Simultaneously Selecting and Estimating Key Model Parameters
• Authors: Kyubaek Yoon, Hojun You, Wei-Ying Wu, Chae Young Lim, Jongeun Choi, Connor Boss, Ahmed Ramadan, John M. Popovich Jr., Jacek Cholewicki, N. Peter Reeves, Clark J. Radcliffe
• Abstract summary: In system identification, estimating parameters of a model using limited observations results in poor identifiability. We propose a new method to simultaneously select and estimate sensitive parameters as key model parameters and fix the remaining parameters to a set of typical values.
• Score: 1.6122433144430324
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In system identification, estimating parameters of a 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 and fix the remaining parameters to a set of typical values. Our method is formulated as a nonlinear least squares estimator with L1-regularization on the deviation of parameters from a set of typical values. First, we provide consistency and oracle properties of the proposed estimator as a theoretical foundation. Second, we provide a novel approach based on Levenberg-Marquardt optimization to numerically find the solution to the formulated problem. Third, to show the effectiveness, we present an application identifying a biomechanical parametric model of a head position tracking task for 10 human subjects from limited data. In a simulation study, the variances of estimated parameters are decreased by 96.1% as compared to that of the estimated parameters without L1-regularization. In an experimental study, our method improves the model interpretation by reducing the number of parameters to be estimated while maintaining variance accounted for (VAF) at above 82.5%. Moreover, the variances of estimated parameters are reduced by 71.1% as compared to that of the estimated parameters without L1-regularization. Our method is 54 times faster than the standard simplex-based optimization to solve the regularized nonlinear regression.

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