Low-rank completion and recovery of correlation matrices
| dc.contributor.advisor | Ouwehand, Peter | |
| dc.contributor.advisor | Mc Walter, Thomas | |
| dc.contributor.author | Ramlall, Chetan K | |
| dc.date.accessioned | 2020-02-13T09:53:43Z | |
| dc.date.available | 2020-02-13T09:53:43Z | |
| dc.date.issued | 2019 | |
| dc.date.updated | 2020-02-13T09:53:18Z | |
| dc.description.abstract | In the pursuit of efficient methods of dimension reduction for multi-factor correlation systems and for sparsely populated and partially observed matrices, the problem of matrix completion within a low-rank framework is of particular significance. This dissertation presents the methods of spectral completion and convex relaxation, which have been successfully applied to the particular problem of lowrank completion and recovery of valid correlation matrices. Numerical testing was performed on the classical exponential and noisy Toeplitz parametrisations and, in addition, to real datasets comprising of FX rates and stock price data. In almost all instances, the method of convex relaxation performed better than spectral methods and achieved the closest and best-fitted low-rank approximations to the true, optimal low-rank matrices (for some rank-n). Furthermore, a dependence was found to exist on which correlation pairs were used as inputs, with the accuracy of the approximations being, in general, directly proportional to the number of input correlations provided to the algorithms. | |
| dc.identifier.apacitation | Ramlall, C. K. (2019). <i>Low-rank completion and recovery of correlation matrices</i>. (). ,Faculty of Commerce ,Division of Actuarial Science. Retrieved from http://hdl.handle.net/11427/31080 | en_ZA |
| dc.identifier.chicagocitation | Ramlall, Chetan K. <i>"Low-rank completion and recovery of correlation matrices."</i> ., ,Faculty of Commerce ,Division of Actuarial Science, 2019. http://hdl.handle.net/11427/31080 | en_ZA |
| dc.identifier.citation | Ramlall, C. 2019. Low-rank completion and recovery of correlation matrices. | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Ramlall, Chetan K AB - In the pursuit of efficient methods of dimension reduction for multi-factor correlation systems and for sparsely populated and partially observed matrices, the problem of matrix completion within a low-rank framework is of particular significance. This dissertation presents the methods of spectral completion and convex relaxation, which have been successfully applied to the particular problem of lowrank completion and recovery of valid correlation matrices. Numerical testing was performed on the classical exponential and noisy Toeplitz parametrisations and, in addition, to real datasets comprising of FX rates and stock price data. In almost all instances, the method of convex relaxation performed better than spectral methods and achieved the closest and best-fitted low-rank approximations to the true, optimal low-rank matrices (for some rank-n). Furthermore, a dependence was found to exist on which correlation pairs were used as inputs, with the accuracy of the approximations being, in general, directly proportional to the number of input correlations provided to the algorithms. DA - 2019 DB - OpenUCT DP - University of Cape Town KW - actuarial science LK - https://open.uct.ac.za PY - 2019 T1 - Low-rank completion and recovery of correlation matrices TI - Low-rank completion and recovery of correlation matrices UR - http://hdl.handle.net/11427/31080 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/31080 | |
| dc.identifier.vancouvercitation | Ramlall CK. Low-rank completion and recovery of correlation matrices. []. ,Faculty of Commerce ,Division of Actuarial Science, 2019 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/31080 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Division of Actuarial Science | |
| dc.publisher.faculty | Faculty of Commerce | |
| dc.subject | actuarial science | |
| dc.title | Low-rank completion and recovery of correlation matrices | |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationname | MPhil |