Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents
We propose a theoretical formalism for inferring the parameters of non-negative physical models via statistical divergence to generalise the fitting process beyond conventional methods. For example, we show that minimising L2 and Kullback–Leibler divergence is equivalent to least squares and maximum...
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| Format: | Article |
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Taylor & Francis Group
2025-12-01
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| Series: | Science and Technology of Advanced Materials: Methods |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27660400.2024.2441102 |
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| author | Yasunobu Ando Shusuke Kasamatsu Suguru Iwasaki Yumi Tanaka |
| author_facet | Yasunobu Ando Shusuke Kasamatsu Suguru Iwasaki Yumi Tanaka |
| author_sort | Yasunobu Ando |
| collection | DOAJ |
| description | We propose a theoretical formalism for inferring the parameters of non-negative physical models via statistical divergence to generalise the fitting process beyond conventional methods. For example, we show that minimising L2 and Kullback–Leibler divergence is equivalent to least squares and maximum likelihood estimation, respectively, for the parameters of non-negative physical models like a probability distribution. To demonstrate this formalism, parameters were estimated in a theoretical model of the thermally stimulated depolarisation current (TSDC), which has a non-negative but complex exponential form. Some technical aspects were also discussed as key points to enable high-throughput fitting of multimode models of TSDC using the proposed formalism, such as the use of the peak temperature as a fitting parameter, which is easily estimated from measured data, instead of a pre-exponential factor that varies by orders of magnitude, and the use of the generalised exponential integral function to speed up the fitting algorithm. |
| format | Article |
| id | doaj-art-774d0406e4444575b2ef396c2758ddc2 |
| institution | Kabale University |
| issn | 2766-0400 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Science and Technology of Advanced Materials: Methods |
| spelling | doaj-art-774d0406e4444575b2ef396c2758ddc22025-01-28T09:18:56ZengTaylor & Francis GroupScience and Technology of Advanced Materials: Methods2766-04002025-12-015110.1080/27660400.2024.2441102Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currentsYasunobu Ando0Shusuke Kasamatsu1Suguru Iwasaki2Yumi Tanaka3Laboratory for Chemistry and Life Science, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, JapanAcademic Assembly (Faculty of Science), Yamagata University, Yamagata-shi, Yamagata, JapanDepartment of industrial Chemistry, Faculty of Engineering, Tokyo University of Science, Tokyo, JapanDepartment of industrial Chemistry, Faculty of Engineering, Tokyo University of Science, Tokyo, JapanWe propose a theoretical formalism for inferring the parameters of non-negative physical models via statistical divergence to generalise the fitting process beyond conventional methods. For example, we show that minimising L2 and Kullback–Leibler divergence is equivalent to least squares and maximum likelihood estimation, respectively, for the parameters of non-negative physical models like a probability distribution. To demonstrate this formalism, parameters were estimated in a theoretical model of the thermally stimulated depolarisation current (TSDC), which has a non-negative but complex exponential form. Some technical aspects were also discussed as key points to enable high-throughput fitting of multimode models of TSDC using the proposed formalism, such as the use of the peak temperature as a fitting parameter, which is easily estimated from measured data, instead of a pre-exponential factor that varies by orders of magnitude, and the use of the generalised exponential integral function to speed up the fitting algorithm.https://www.tandfonline.com/doi/10.1080/27660400.2024.2441102Machine learningEM algorithmthermally stimulated depolarization currentsstatistical divergencemaximum likelihood estimationnon-linear regression |
| spellingShingle | Yasunobu Ando Shusuke Kasamatsu Suguru Iwasaki Yumi Tanaka Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents Science and Technology of Advanced Materials: Methods Machine learning EM algorithm thermally stimulated depolarization currents statistical divergence maximum likelihood estimation non-linear regression |
| title | Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents |
| title_full | Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents |
| title_fullStr | Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents |
| title_full_unstemmed | Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents |
| title_short | Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents |
| title_sort | fitting of nonnegative physical models based on statistical divergence application to thermally stimulated depolarization currents |
| topic | Machine learning EM algorithm thermally stimulated depolarization currents statistical divergence maximum likelihood estimation non-linear regression |
| url | https://www.tandfonline.com/doi/10.1080/27660400.2024.2441102 |
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