2023-03-31T13:07:04Z
https://repository.nii.ac.jp/oai
oai:repository.nii.ac.jp:02000370
2023-01-11T05:58:17Z
136
NII Technical Report (NII-2020-002E)：Cluster Gauss-Newton method for finding multiple approximate minimisers of nonlinear least squares problems with applications to parameter estimation of pharmacokinetic models
青木, 康憲
Aoki, Yasunori
速水, 謙
Hayami, Ken
年本, 広太
Toshimoto, Kota
杉山, 雄一
Sugiyama, Yuichi
テクニカルレポート
Technical Report
Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems. Typically these problems are solved numerically using iterative methods. The local minimiser obtained using these iterative methods usually depends on the choice of the initial iterate. Thus, the estimated parameter and subsequent analyses using it depend on the choice of the initial iterate. One way to reduce the analysis bias due to the choice of the initial iterate is to repeat the algorithm from multiple initial iterates (i.e. use a multi-start method). However, the procedure can be computationally intensive and is not always used in practice. To overcome this problem, we pro-pose the Cluster Gauss-Newton (CGN) method, an e cient algorithm for nding multiple approximate minimisers of nonlinear-least squares problems. CGN simultaneously solves the nonlinear least squares problem from multiple initial iterates. Then, CGN iteratively improves the solutions from these initial iterates similarly to the Gauss-Newton method. However, it uses a global linear approximation instead of the Jacobian. The global linear approximations are computed collectively among all the iterates to minimise the computational cost. We use physiologically based pharmacokinetic (PBPK) models used in pharmaceutical drug development to demonstrate its use and show that CGN is computationally more e cient and more robust against local minima compared to the standard Levenberg-Marquardt method, as well as state-of-the art multi-start and derivative-free methods.
国立情報学研究所
2020-04-13
eng
departmental bulletin paper
https://doi.org/10.20736/0002000370
https://repository.nii.ac.jp/records/2000370
10.20736/0002000370
1346-5597
NIIテクニカル・レポート
NII Technical Report
1
32
https://repository.nii.ac.jp/record/2000370/files/20-002E.pdf
application/pdf
6.4 MB
2022-06-09