An Entropic Approach to Constrained Linear Regression
We introduce a novel entropy minimization approach for the solution of constrained linear regression problems. Rather than minimizing the quadratic error, our method minimizes the Fermi–Dirac entropy, with the problem data incorporated as constraints. In addition to providing a solution to the linea...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/3/456 |
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| author | Argimiro Arratia Henryk Gzyl |
| author_facet | Argimiro Arratia Henryk Gzyl |
| author_sort | Argimiro Arratia |
| collection | DOAJ |
| description | We introduce a novel entropy minimization approach for the solution of constrained linear regression problems. Rather than minimizing the quadratic error, our method minimizes the Fermi–Dirac entropy, with the problem data incorporated as constraints. In addition to providing a solution to the linear regression problem, this approach also estimates the measurement error. The only prior assumption made about the errors is analogous to the assumption made about the unknown regression coefficients: specifically, the size of the interval within which they are expected to lie. We compare the results of our approach with those obtained using the disciplined convex optimization methodology. Furthermore, we address consistency issues and present examples to illustrate the effectiveness of our method. |
| format | Article |
| id | doaj-art-eeea9bd001b048a4ad9531bbea92fea9 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-eeea9bd001b048a4ad9531bbea92fea92025-08-20T02:48:07ZengMDPI AGMathematics2227-73902025-01-0113345610.3390/math13030456An Entropic Approach to Constrained Linear RegressionArgimiro Arratia0Henryk Gzyl1Computer Science, Polytechnical University of Catalonia, 08034 Barcelona, SpainCentro de Finanzas IESA, Caracas 1010, VenezuelaWe introduce a novel entropy minimization approach for the solution of constrained linear regression problems. Rather than minimizing the quadratic error, our method minimizes the Fermi–Dirac entropy, with the problem data incorporated as constraints. In addition to providing a solution to the linear regression problem, this approach also estimates the measurement error. The only prior assumption made about the errors is analogous to the assumption made about the unknown regression coefficients: specifically, the size of the interval within which they are expected to lie. We compare the results of our approach with those obtained using the disciplined convex optimization methodology. Furthermore, we address consistency issues and present examples to illustrate the effectiveness of our method.https://www.mdpi.com/2227-7390/13/3/456constrained linear regressionFermi–Dirac entropyconvex optimizationill-posed inverse problems |
| spellingShingle | Argimiro Arratia Henryk Gzyl An Entropic Approach to Constrained Linear Regression Mathematics constrained linear regression Fermi–Dirac entropy convex optimization ill-posed inverse problems |
| title | An Entropic Approach to Constrained Linear Regression |
| title_full | An Entropic Approach to Constrained Linear Regression |
| title_fullStr | An Entropic Approach to Constrained Linear Regression |
| title_full_unstemmed | An Entropic Approach to Constrained Linear Regression |
| title_short | An Entropic Approach to Constrained Linear Regression |
| title_sort | entropic approach to constrained linear regression |
| topic | constrained linear regression Fermi–Dirac entropy convex optimization ill-posed inverse problems |
| url | https://www.mdpi.com/2227-7390/13/3/456 |
| work_keys_str_mv | AT argimiroarratia anentropicapproachtoconstrainedlinearregression AT henrykgzyl anentropicapproachtoconstrainedlinearregression AT argimiroarratia entropicapproachtoconstrainedlinearregression AT henrykgzyl entropicapproachtoconstrainedlinearregression |