Search results for "uniquene"
showing 2 items of 212 documents
La Géométrie pour l'Unicité, la Parcimonie et l'Appariement des Estimateurs Pénalisés
2022
During the talk we will give a necessary and sufficient condition for the uniqueness of a penalized least squares estimator whose penalty term is a polyhedral norm. Our results cover many methods including the OSCAR, SLOPE and LASSO estimators as well as the related method of basis pursuit. The geometrical condition for uniqueness involves how the row span of the design matrix intersects the faces of the dual normunit ball. Theoretical results on sparsity by LASSO and basis pursuit estimators are deduced from this condition via the characterization of accessible sign vectors for these two methods.
Assessing the conservation priority of freshwater lake sites based on taxonomic, functional and environmental uniqueness
2022
Aim We propose a novel approach that considers taxonomic uniqueness, functional uniqueness and environmental uniqueness and show how it can be used in guiding conservation planning. We illustrate the approach using data for lake biota and environment. Location Lake Puruvesi, Finland. Methods We sampled macrophytes and macroinvertebrates from the same 18 littoral sites. By adapting the original “ecological uniqueness” approach, we used distance-based methods to calculate measures of taxonomic (LCBD–t), functional (LCBD–f) and environmental (LCEH) uniqueness for each site. We also considered the numbers and locations of the sites needed to protect up to 70% of total variation in taxonomic, fu…