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LASSO - simultaneous shrinkage and selection via the L1 norm
Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2014.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2015
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| _version_ | 1867613631325143040 |
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| access_status_str | Open Access |
| author2 | Kanfer, F.H.J. (Frans) |
| author_browse | Kanfer, F.H.J. (Frans) |
| author_facet | Kanfer, F.H.J. (Frans) |
| collection | Thesis |
| dc_rights_str_mv | © 2014 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2014. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/44244 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:12.888Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/44244 LASSO - simultaneous shrinkage and selection via the L1 norm Kanfer, F.H.J. (Frans) Millard, Sollie M. Kirkland, Lisa-Ann Statistics UCTD Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2014. Two major purposes of regression models are explanation and prediction of scientific phenomena. Explanation is obtained by producing interpretable models through variable selection, while prediction accuracy is optimised by balancing the bias and variance of predictions. This dissertation explores the LASSO, a shrinkage method that simultaneously performs selection and estimation, yielding interpretable models with high prediction accuracy. By penalizing the regression model, the variance is substantially reduced and sparsity is promoted by using the L1 norm. It often outperforms traditional methods like subset selection and ridge regression, each focusing either on variable selection or prediction, respectively. The LASSO has favourable statistical properties and can also be applied to high dimensional data. Applied in two-stage procedures, the bias is controlled to achieve consistency for both prediction and selection. Concave penalties reduce the bias more effectively by applying different penalty functions over fixed ranges of each coefficient’s size. Adaptations of the LASSO penalty allow incorporating different structures between predictors, such as ordering predictors in a meaningful way or including known groups of predictors like dummy variables or polynomials. Penalties combining the L1 norm with other norms allow the identification of unknown groups of correlated variables. Overall the LASSO provides an elegant foundation for a class of methods which improves the way that sparse regression problems are solved. lk2015 Statistics MSc (Mathematical Statistics) unrestricted 2015-04-07T11:04:14Z 2015-04-07T11:04:14Z 2015-04 2014 Mini Dissertation Kirkland, L 2014, LASSO - Simultaneous shrinkage and selection via the L1 norm, Masters Thesis, University of Pretoria, Pretoria http://hdl.handle.net/2263/44244 http://hdl.handle.net/2263/44244 en © 2014 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Statistics UCTD LASSO - simultaneous shrinkage and selection via the L1 norm |
| title | LASSO - simultaneous shrinkage and selection via the L1 norm |
| title_full | LASSO - simultaneous shrinkage and selection via the L1 norm |
| title_fullStr | LASSO - simultaneous shrinkage and selection via the L1 norm |
| title_full_unstemmed | LASSO - simultaneous shrinkage and selection via the L1 norm |
| title_short | LASSO - simultaneous shrinkage and selection via the L1 norm |
| title_sort | lasso simultaneous shrinkage and selection via the l1 norm |
| topic | Statistics UCTD |
| url | http://hdl.handle.net/2263/44244 |