Neural Networks as a Convex Problem
A Master of Science thesis in Mathematics by Baha Khalil entitled, "Neural Networks as a Convex Problem," submitted in September 2016. Thesis advisor is Dr. Dmitry Efimov. Soft and hard copy available.
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | doctoralThesis |
| منشور في: |
2016
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/8493 |
| الوسوم: |
إضافة وسم
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| _version_ | 1864513442004598784 |
|---|---|
| author | Khalil, Baha |
| author_facet | Khalil, Baha |
| author_role | author |
| dc.contributor.none.fl_str_mv | Efimov, Dmitry |
| dc.creator.none.fl_str_mv | Khalil, Baha |
| dc.date.none.fl_str_mv | 2016-10-10T05:57:32Z 2016-10-10T05:57:32Z 2016-09 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2016.08 http://hdl.handle.net/11073/8493 |
| dc.language.none.fl_str_mv | en_US |
| dc.subject.none.fl_str_mv | Neural Networks Convex Optimization Gauss-Newton Matrix Neural networks (Computer science) Mathematical optimization Convex functions |
| dc.title.none.fl_str_mv | Neural Networks as a Convex Problem |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/doctoralThesis |
| description | A Master of Science thesis in Mathematics by Baha Khalil entitled, "Neural Networks as a Convex Problem," submitted in September 2016. Thesis advisor is Dr. Dmitry Efimov. Soft and hard copy available. |
| format | doctoralThesis |
| id | aus_5226dce90ff0f32b3cda331b6a3f0a5c |
| identifier_str_mv | 29.232-2016.08 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/8493 |
| publishDate | 2016 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Neural Networks as a Convex ProblemKhalil, BahaNeural NetworksConvex OptimizationGauss-Newton MatrixNeural networks (Computer science)Mathematical optimizationConvex functionsA Master of Science thesis in Mathematics by Baha Khalil entitled, "Neural Networks as a Convex Problem," submitted in September 2016. Thesis advisor is Dr. Dmitry Efimov. Soft and hard copy available.We reformulated the problem of training the neural networks model into a convex optimization problem by performing a local quadratic expansion of the cost function and adding the necessary constraints. We designed a new algorithm that extends the back propagation algorithm for parameters estimation by using second-order optimization methods. We computed the second order mixed partial derivatives of the cost function for a single hidden layer neural network model to construct the Hessian matrix. We used the Gauss-Newton approximation instead of the Hessian matrix to avoid the analytical computation of the second order derivative terms for higher order neural network topologies. To compare the accuracy and computational complexity of our proposed algorithm versus the standard back propagation we tested both algorithms in different applications, such as: regression, classification, and ranking.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Efimov, Dmitry2016-10-10T05:57:32Z2016-10-10T05:57:32Z2016-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2016.08http://hdl.handle.net/11073/8493en_USoai:repository.aus.edu:11073/84932025-06-26T12:25:59Z |
| spellingShingle | Neural Networks as a Convex Problem Khalil, Baha Neural Networks Convex Optimization Gauss-Newton Matrix Neural networks (Computer science) Mathematical optimization Convex functions |
| status_str | publishedVersion |
| title | Neural Networks as a Convex Problem |
| title_full | Neural Networks as a Convex Problem |
| title_fullStr | Neural Networks as a Convex Problem |
| title_full_unstemmed | Neural Networks as a Convex Problem |
| title_short | Neural Networks as a Convex Problem |
| title_sort | Neural Networks as a Convex Problem |
| topic | Neural Networks Convex Optimization Gauss-Newton Matrix Neural networks (Computer science) Mathematical optimization Convex functions |
| url | http://hdl.handle.net/11073/8493 |