Fundamentals of convex optimization for compositional data
Many of the most popular statistical techniques incorporate optimisation problems in their inner workings. A convex optimisation problem is defined as the problem of minimising a convex function over a convex set. When traditional methods are applied to compositional data, misleading and incoherent...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/421365 |
| Online Access: | https://hdl.handle.net/2117/421365 https://dx.doi.org/10.57645/20.8080.02.11 |
| Access Level: | Open access |
| Keyword: | Mathematical statistics compositional data logratio simplex proportion function convexity optimisation Estadística matemàtica Classificació AMS::62 Statistics Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
| Summary: | Many of the most popular statistical techniques incorporate optimisation problems in their inner workings. A convex optimisation problem is defined as the problem of minimising a convex function over a convex set. When traditional methods are applied to compositional data, misleading and incoherent results could be obtained. In this paper, we fill a gap in the specialised literature by introducing and rigorously defining novel concepts of convex optimisation for compositional data according to the Aitchison geometry. Convex sets and convex functions on the simplex are defined and illustrated. |
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