Best Subset Solution Path for Linear Dimension Reduction Models using Continuous Optimization

• DOI: 10.48550/arxiv.2403.20007
• Publication Date: 2024-03-29
• Authors: Benoît Liquet; Sarat Moka; Samuel Müller
• Keywords: Methodology (stat.ME); FOS: Computer and information sciences; Statistics - Other Statistics; Other Statistics (stat.OT); 0101 mathematics; Statistics - Computation; 01 natural sciences; Statistics - Methodology; Computation (stat.CO)

The selection of best variables is a challenging problem in supervised and unsupervised learning, especially high dimensional contexts where the number usually much larger than observations. In this paper, we focus on two multivariate statistical methods: principal components analysis partial least squares. Both approaches are popular linear dimension-reduction methods with numerous applications several fields including genomics, biology, environmental science, engineering. particular, these build components, new that combinations all original variables. A main drawback difficulty to interpret them when large. To define from most relevant variables, propose cast subset solution path method into component square frameworks. We offer alternative by exploiting continuous optimization algorithm for path. Empirical studies show efficacy our approach providing usage further exposed through real datasets. first dataset analyzed using principle while second based framework.