Search results for "Basis pursuit"
showing 4 items of 4 documents
A systematic comparison of kinetic modelling methods generating parametric maps for [11C]-(R)-PK11195
2006
[(11)C]-(R)-PK11195 is presently the most widely used radiotracer for the monitoring of microglia activity in the central nervous system (CNS). Microglia, the resident immune cells of the brain, play a critical role in acute and chronic diseases of the central nervous system and in host defence against neoplasia. The purpose of this investigation was to evaluate the reliability and sensitivity of five kinetic modelling methods for the formation of parametric maps from dynamic [(11)C]-(R)-PK11195 studies. The methods we tested were the simplified reference tissue model (SRTM), basis pursuit, a simple target-to-reference ratio, the Logan plot and a wavelet based Logan plot. For the reliabilit…
Using the Theory of Regular Functions to Formally Prove the ε-Optimality of Discretized Pursuit Learning Algorithms
2014
Learning Automata LA can be reckoned to be the founding algorithms on which the field of Reinforcement Learning has been built. Among the families of LA, Estimator Algorithms EAs are certainly the fastest, and of these, the family of Pursuit Algorithms PAs are the pioneering work. It has recently been reported that the previous proofs for e-optimality for all the reported algorithms in the family of PAs have been flawed. We applaud the researchers who discovered this flaw, and who further proceeded to rectify the proof for the Continuous Pursuit Algorithm CPA. The latter proof, though requires the learning parameter to be continuously changing, is, to the best of our knowledge, the current …
On the sign recovery by LASSO, thresholded LASSO and thresholded Basis Pursuit Denoising
2020
Basis Pursuit (BP), Basis Pursuit DeNoising (BPDN), and LASSO are popular methods for identifyingimportant predictors in the high-dimensional linear regression model Y = Xβ + ε. By definition, whenε = 0, BP uniquely recovers β when Xβ = Xb and β different than b implies L1 norm of β is smaller than the L1 norm of b (identifiability condition). Furthermore, LASSO can recover the sign of β only under a much stronger irrepresentability condition. Meanwhile, it is known that the model selection properties of LASSO can be improved by hard-thresholdingits estimates. This article supports these findings by proving that thresholded LASSO, thresholded BPDNand thresholded BP recover the sign of β in …
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.