Some Thoughts About the Design of Loss Functions
The choice and design of loss functions is discussed. Particularly when computational methods like cross-validation are applied, there is no need to stick to “standard” loss functions such as the L2-loss (squared loss). Our main message is that the choice of a loss function in a practical situation...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2007-03-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/40 |
| _version_ | 1817999388519170048 |
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| author | Christian Hennig Mahmut Kutlukaya |
| author_facet | Christian Hennig Mahmut Kutlukaya |
| author_sort | Christian Hennig |
| collection | DOAJ |
| description |
The choice and design of loss functions is discussed. Particularly when computational methods like cross-validation are applied, there is no need to stick to “standard” loss functions such as the L2-loss (squared loss). Our main message is that the choice of a loss function in a practical situation is the translation of an informal aim or interest that a researcher may have into the formal language of mathematics. The choice of a loss function cannot be formalized as a solution of a mathematical decision problem in itself. An illustrative case study about the location of branches of a chain of restaurants is given. Statistical aspects of loss functions are treated, such as the distinction between applications of loss functions to prediction and estimation problems and the direct definition of estimators to minimize loss functions. The impact of subjective decisions to the design of loss functions is also emphasized and discussed.
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| first_indexed | 2024-04-14T03:08:06Z |
| format | Article |
| id | doaj.art-4919f0cded534179b9404bb27569db87 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T03:08:06Z |
| publishDate | 2007-03-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-4919f0cded534179b9404bb27569db872022-12-22T02:15:40ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712007-03-015110.57805/revstat.v5i1.40Some Thoughts About the Design of Loss FunctionsChristian Hennig 0Mahmut Kutlukaya 1University College LondonBanking Regulation and Supervision Agency The choice and design of loss functions is discussed. Particularly when computational methods like cross-validation are applied, there is no need to stick to “standard” loss functions such as the L2-loss (squared loss). Our main message is that the choice of a loss function in a practical situation is the translation of an informal aim or interest that a researcher may have into the formal language of mathematics. The choice of a loss function cannot be formalized as a solution of a mathematical decision problem in itself. An illustrative case study about the location of branches of a chain of restaurants is given. Statistical aspects of loss functions are treated, such as the distinction between applications of loss functions to prediction and estimation problems and the direct definition of estimators to minimize loss functions. The impact of subjective decisions to the design of loss functions is also emphasized and discussed. https://revstat.ine.pt/index.php/REVSTAT/article/view/40predictionestimationdecision theoryM-estimatorMM-estimatorlinear regression |
| spellingShingle | Christian Hennig Mahmut Kutlukaya Some Thoughts About the Design of Loss Functions Revstat Statistical Journal prediction estimation decision theory M-estimator MM-estimator linear regression |
| title | Some Thoughts About the Design of Loss Functions |
| title_full | Some Thoughts About the Design of Loss Functions |
| title_fullStr | Some Thoughts About the Design of Loss Functions |
| title_full_unstemmed | Some Thoughts About the Design of Loss Functions |
| title_short | Some Thoughts About the Design of Loss Functions |
| title_sort | some thoughts about the design of loss functions |
| topic | prediction estimation decision theory M-estimator MM-estimator linear regression |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/40 |
| work_keys_str_mv | AT christianhennig somethoughtsaboutthedesignoflossfunctions AT mahmutkutlukaya somethoughtsaboutthedesignoflossfunctions |