Combining Data Envelopment Analysis and Machine Learning
Data Envelopment Analysis (DEA) is one of the most used non-parametric techniques for technical efficiency assessment. DEA is exclusively concerned about the minimization of the empirical error, satisfying, at the same time, some shape constraints (convexity and free disposability). Unfortunately, b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/6/909 |
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| author | Nadia M. Guerrero Juan Aparicio Daniel Valero-Carreras |
| author_facet | Nadia M. Guerrero Juan Aparicio Daniel Valero-Carreras |
| author_sort | Nadia M. Guerrero |
| collection | DOAJ |
| description | Data Envelopment Analysis (DEA) is one of the most used non-parametric techniques for technical efficiency assessment. DEA is exclusively concerned about the minimization of the empirical error, satisfying, at the same time, some shape constraints (convexity and free disposability). Unfortunately, by construction, DEA is a descriptive methodology that is not concerned about preventing overfitting. In this paper, we introduce a new methodology that allows for estimating polyhedral technologies following the Structural Risk Minimization (SRM) principle. This technique is called Data Envelopment Analysis-based Machines (DEAM). Given that the new method controls the generalization error of the model, the corresponding estimate of the technology does not suffer from overfitting. Moreover, the notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula>-insensitivity is also introduced, generating a new and more robust definition of technical efficiency. Additionally, we show that DEAM can be seen as a machine learning-type extension of DEA, satisfying the same microeconomic postulates except for minimal extrapolation. Finally, the performance of DEAM is evaluated through simulations. We conclude that the frontier estimator derived from DEAM is better than that associated with DEA. The bias and mean squared error obtained for DEAM are smaller in all the scenarios analyzed, regardless of the number of variables and DMUs. |
| first_indexed | 2024-03-09T13:26:47Z |
| format | Article |
| id | doaj.art-edf75629d4f4477094e09cda77e761d0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:26:47Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-edf75629d4f4477094e09cda77e761d02023-11-30T21:23:53ZengMDPI AGMathematics2227-73902022-03-0110690910.3390/math10060909Combining Data Envelopment Analysis and Machine LearningNadia M. Guerrero0Juan Aparicio1Daniel Valero-Carreras2Center of Operations Research (CIO), Miguel Hernandez University of Elche (UMH), 03202 Elche, SpainCenter of Operations Research (CIO), Miguel Hernandez University of Elche (UMH), 03202 Elche, SpainCenter of Operations Research (CIO), Miguel Hernandez University of Elche (UMH), 03202 Elche, SpainData Envelopment Analysis (DEA) is one of the most used non-parametric techniques for technical efficiency assessment. DEA is exclusively concerned about the minimization of the empirical error, satisfying, at the same time, some shape constraints (convexity and free disposability). Unfortunately, by construction, DEA is a descriptive methodology that is not concerned about preventing overfitting. In this paper, we introduce a new methodology that allows for estimating polyhedral technologies following the Structural Risk Minimization (SRM) principle. This technique is called Data Envelopment Analysis-based Machines (DEAM). Given that the new method controls the generalization error of the model, the corresponding estimate of the technology does not suffer from overfitting. Moreover, the notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula>-insensitivity is also introduced, generating a new and more robust definition of technical efficiency. Additionally, we show that DEAM can be seen as a machine learning-type extension of DEA, satisfying the same microeconomic postulates except for minimal extrapolation. Finally, the performance of DEAM is evaluated through simulations. We conclude that the frontier estimator derived from DEAM is better than that associated with DEA. The bias and mean squared error obtained for DEAM are smaller in all the scenarios analyzed, regardless of the number of variables and DMUs.https://www.mdpi.com/2227-7390/10/6/909data envelopment analysisPAC learningsupport vector regressionmachine learningstructural risk minimization |
| spellingShingle | Nadia M. Guerrero Juan Aparicio Daniel Valero-Carreras Combining Data Envelopment Analysis and Machine Learning Mathematics data envelopment analysis PAC learning support vector regression machine learning structural risk minimization |
| title | Combining Data Envelopment Analysis and Machine Learning |
| title_full | Combining Data Envelopment Analysis and Machine Learning |
| title_fullStr | Combining Data Envelopment Analysis and Machine Learning |
| title_full_unstemmed | Combining Data Envelopment Analysis and Machine Learning |
| title_short | Combining Data Envelopment Analysis and Machine Learning |
| title_sort | combining data envelopment analysis and machine learning |
| topic | data envelopment analysis PAC learning support vector regression machine learning structural risk minimization |
| url | https://www.mdpi.com/2227-7390/10/6/909 |
| work_keys_str_mv | AT nadiamguerrero combiningdataenvelopmentanalysisandmachinelearning AT juanaparicio combiningdataenvelopmentanalysisandmachinelearning AT danielvalerocarreras combiningdataenvelopmentanalysisandmachinelearning |