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...

Descripción completa

Detalles Bibliográficos
Autores: Saperas Riera, Jordi|||0000-0001-8221-4325, Martín-Fernández, Josep-Antoni|||0000-0003-2366-1592, Mateu-Figueras, Glòria|||0000-0002-2477-2764
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:285315
Acceso en línea:https://ddd.uab.cat/record/285315
https://dx.doi.org/urn:doi:10.57645/20.8080.02.11
Access Level:acceso abierto
Palabra clave:Compositional data
Logratio
Simplex
Proportion
Function
Convexity
Optimisation
Descripción
Sumario: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.